diff --git a/CHANGELOG.md b/CHANGELOG.md
index 6f12dda513629..269f8e5f27a4e 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -288,6 +288,9 @@ The format is based on [Keep a Changelog](http://keepachangelog.com/en/1.0.0/).
 - Updated error message for interactive incompatible plugins ([#9896](https://github.com/PyTorchLightning/pytorch-lightning/pull/9896))
 
 
+- Updated several places in the loops and trainer to access `training_type_plugin` directly instead of `accelerator` ([#9901](https://github.com/PyTorchLightning/pytorch-lightning/pull/9901))
+
+
 ### Deprecated
 
 - Deprecated trainer argument `terminate_on_nan` in favour of `detect_anomaly`([#9175](https://github.com/PyTorchLightning/pytorch-lightning/pull/9175))
diff --git a/pytorch_lightning/accelerators/accelerator.py b/pytorch_lightning/accelerators/accelerator.py
index cfed45e1db186..541cf5de3be2b 100644
--- a/pytorch_lightning/accelerators/accelerator.py
+++ b/pytorch_lightning/accelerators/accelerator.py
@@ -59,7 +59,18 @@ def __init__(self, precision_plugin: PrecisionPlugin, training_type_plugin: Trai
         self.optimizer_frequencies: List = []
 
     def connect(self, model: "pl.LightningModule") -> None:
-        """Transfers ownership of the model to this plugin."""
+        """Transfers ownership of the model to this plugin.
+
+        See deprecation warning below.
+
+        .. deprecated:: v1.5
+            This method is deprecated in v1.5 and will be removed in v1.6.
+            Please call `training_type_plugin.on_train_batch_start` directly.
+        """
+        rank_zero_deprecation(
+            "`Accelerator.connect` is deprecated in v1.5 and will be removed in v1.6. "
+            "`connect` logic is implemented directly in the `TrainingTypePlugin` implementations."
+        )
         self.training_type_plugin.connect(model)
 
     def setup_environment(self) -> None:
@@ -82,12 +93,39 @@ def setup(self, trainer: "pl.Trainer") -> None:
         self.setup_precision_plugin()
 
     def start_training(self, trainer: "pl.Trainer") -> None:
+        """
+        .. deprecated:: v1.5
+            This method is deprecated in v1.5 and will be removed in v1.6.
+            Please call `training_type_plugin.start_training` directly.
+        """
+        rank_zero_deprecation(
+            "`Accelerator.start_training` is deprecated in v1.5 and will be removed in v1.6. "
+            "`start_training` logic is implemented directly in the `TrainingTypePlugin` implementations."
+        )
         self.training_type_plugin.start_training(trainer)
 
     def start_evaluating(self, trainer: "pl.Trainer") -> None:
+        """
+        .. deprecated:: v1.5
+            This method is deprecated in v1.5 and will be removed in v1.6.
+            Please call `training_type_plugin.start_evaluating` directly.
+        """
+        rank_zero_deprecation(
+            "`Accelerator.start_evaluating` is deprecated in v1.5 and will be removed in v1.6. "
+            "`start_evaluating` logic is implemented directly in the `TrainingTypePlugin` implementations."
+        )
         self.training_type_plugin.start_evaluating(trainer)
 
     def start_predicting(self, trainer: "pl.Trainer") -> None:
+        """
+        .. deprecated:: v1.5
+            This method is deprecated in v1.5 and will be removed in v1.6.
+            Please call `training_type_plugin.start_predicting` directly.
+        """
+        rank_zero_deprecation(
+            "`Accelerator.start_predicting` is deprecated in v1.5 and will be removed in v1.6. "
+            "`start_predicting` logic is implemented directly in the `TrainingTypePlugin` implementations."
+        )
         self.training_type_plugin.start_predicting(trainer)
 
     def pre_dispatch(self, trainer: "pl.Trainer") -> None:
@@ -177,6 +215,15 @@ def training_step(self, step_kwargs: Dict[str, Union[Any, int]]) -> STEP_OUTPUT:
             return self.training_type_plugin.training_step(*step_kwargs.values())
 
     def post_training_step(self) -> None:
+        """
+        .. deprecated:: v1.5
+            This method is deprecated in v1.5 and will be removed in v1.6.
+            Please call `training_type_plugin.post_training_step` directly.
+        """
+        rank_zero_deprecation(
+            "`Accelerator.post_training_step` is deprecated in v1.5 and will be removed in v1.6. "
+            "`post_training_step` logic is implemented directly in the `TrainingTypePlugin` implementations."
+        )
         self.training_type_plugin.post_training_step()
 
     def validation_step(self, step_kwargs: Dict[str, Union[Any, int]]) -> Optional[STEP_OUTPUT]:
@@ -206,25 +253,49 @@ def predict_step(self, step_kwargs: Dict[str, Union[Any, int]]) -> STEP_OUTPUT:
     def training_step_end(self, output: STEP_OUTPUT) -> STEP_OUTPUT:
         """A hook to do something at the end of the training step.
 
+        .. deprecated:: v1.5
+            This method is deprecated in v1.5 and will be removed in v1.6.
+            Please call `training_type_plugin.training_step_end` directly.
+
         Args:
             output: the output of the training step
         """
+        rank_zero_deprecation(
+            "`Accelerator.training_step_end` is deprecated in v1.5 and will be removed in v1.6. "
+            "`training_step_end` logic is implemented directly in the `TrainingTypePlugin` implementations."
+        )
         return self.training_type_plugin.training_step_end(output)
 
     def test_step_end(self, output: Optional[STEP_OUTPUT]) -> Optional[STEP_OUTPUT]:
         """A hook to do something at the end of the test step.
 
+        .. deprecated:: v1.5
+            This method is deprecated in v1.5 and will be removed in v1.6.
+            Please call `training_type_plugin.test_step_end` directly.
+
         Args:
             output: the output of the test step
         """
+        rank_zero_deprecation(
+            "`Accelerator.test_step_end` is deprecated in v1.5 and will be removed in v1.6. "
+            "`test_step_end` logic is implemented directly in the `TrainingTypePlugin` implementations."
+        )
         return self.training_type_plugin.test_step_end(output)
 
     def validation_step_end(self, output: Optional[STEP_OUTPUT]) -> Optional[STEP_OUTPUT]:
         """A hook to do something at the end of the validation step.
 
+        .. deprecated:: v1.5
+            This method is deprecated in v1.5 and will be removed in v1.6.
+            Please call `training_type_plugin.validation_step_end` directly.
+
         Args:
             output: the output of the validation step
         """
+        rank_zero_deprecation(
+            "`Accelerator.validation_step_end` is deprecated in v1.5 and will be removed in v1.6. "
+            "`validation_step_end` logic is implemented directly in the `TrainingTypePlugin` implementations."
+        )
         return self.training_type_plugin.validation_step_end(output)
 
     def backward(self, closure_loss: Tensor, *args: Any, **kwargs: Any) -> Tensor:
@@ -330,19 +401,27 @@ def optimizer_state(self, optimizer: Optimizer) -> Dict[str, Tensor]:
     def lightning_module_state_dict(self) -> Dict[str, Union[Any, Tensor]]:
         """Returns state of model.
 
+        .. deprecated:: v1.5
+            This method is deprecated in v1.5 and will be removed in v1.6.
+            Please call `training_type_plugin.lightning_module_state_dict` directly.
+
         Allows for syncing/collating model state from processes in custom plugins.
         """
+        rank_zero_deprecation(
+            "`Accelerator.lightning_module_state_dict` is deprecated in v1.5 and will be removed in v1.6. "
+            "`lightning_module_state_dict` logic is implemented directly in the `TrainingTypePlugin` implementations."
+        )
         return self.training_type_plugin.lightning_module_state_dict()
 
     def barrier(self, name: Optional[str] = None) -> None:
         """
         .. deprecated:: v1.5
             This method is deprecated in v1.5 and will be removed in v1.6.
-            Please call ``training_type_plugin.barrier`` directly.
+            Please call `training_type_plugin.barrier` directly.
         """
         rank_zero_deprecation(
             "`Accelerator.barrier` is deprecated in v1.5 and will be removed in v1.6. "
-            "Barrier logic is implemented directly in the `TrainingTypePlugin` implementations."
+            "`Barrier` logic is implemented directly in the `TrainingTypePlugin` implementations."
         )
         self.training_type_plugin.barrier(name=name)
 
@@ -352,7 +431,7 @@ def broadcast(self, obj: object, src: int = 0) -> object:
 
         .. deprecated:: v1.5
             This method is deprecated in v1.5 and will be removed in v1.6.
-            Please call ``training_type_plugin.broadcast`` directly.
+            Please call `training_type_plugin.broadcast` directly.
 
         Args:
             obj: Object to broadcast to all process, usually a tensor or collection of tensors.
@@ -360,7 +439,7 @@ def broadcast(self, obj: object, src: int = 0) -> object:
         """
         rank_zero_deprecation(
             "`Accelerator.broadcast` is deprecated in v1.5 and will be removed in v1.6. "
-            "Broadcast logic is implemented directly in the `TrainingTypePlugin` implementations."
+            "`Broadcast` logic is implemented directly in the `TrainingTypePlugin` implementations."
         )
         return self.training_type_plugin.broadcast(obj, src)
 
@@ -369,7 +448,7 @@ def all_gather(self, tensor: Tensor, group: Optional[Any] = None, sync_grads: bo
 
         .. deprecated:: v1.5
             This method is deprecated in v1.5 and will be removed in v1.6.
-            Please call ``training_type_plugin.all_gather`` directly.
+            Please call `training_type_plugin.all_gather` directly.
 
         Args:
             tensor: tensor of shape (batch, ...)
@@ -381,24 +460,40 @@ def all_gather(self, tensor: Tensor, group: Optional[Any] = None, sync_grads: bo
         """
         rank_zero_deprecation(
             "`Accelerator.all_gather` is deprecated in v1.5 and will be removed in v1.6. "
-            "All-gather logic is implemented directly in the `TrainingTypePlugin` implementations."
+            "`all_gather` logic is implemented directly in the `TrainingTypePlugin` implementations."
         )
         return self.training_type_plugin.all_gather(tensor, group=group, sync_grads=sync_grads)
 
     def process_dataloader(self, dataloader: Union[Iterable, DataLoader]) -> Union[Iterable, DataLoader]:
         """Wraps the dataloader if necessary.
 
+        .. deprecated:: v1.5
+            This method is deprecated in v1.5 and will be removed in v1.6.
+            Please call `training_type_plugin.process_dataloader` directly.
+
         Args:
             dataloader: iterable. Ideally of type: :class:`torch.utils.data.DataLoader`
         """
+        rank_zero_deprecation(
+            "`Accelerator.process_dataloader` is deprecated in v1.5 and will be removed in v1.6. "
+            "`process_dataloader` logic is implemented directly in the `TrainingTypePlugin` implementations."
+        )
         return self.training_type_plugin.process_dataloader(dataloader)
 
     @property
     def results(self) -> Any:
         """The results of the last run will be cached within the training type plugin.
 
+        .. deprecated:: v1.5
+            This property is deprecated in v1.5 and will be removed in v1.6.
+            Please call `training_type_plugin.results` directly.
+
         In distributed training, we make sure to transfer the results to the appropriate master process.
         """
+        rank_zero_deprecation(
+            "`Accelerator.results` is deprecated in v1.5 and will be removed in v1.6. "
+            "Accesse results directly from the `TrainingTypePlugin`."
+        )
         return self.training_type_plugin.results
 
     @contextlib.contextmanager
@@ -417,10 +512,18 @@ def model_sharded_context(self) -> Generator[None, None, None]:
     def save_checkpoint(self, checkpoint: Dict[str, Any], filepath: _PATH) -> None:
         """Save model/training states as a checkpoint file through state-dump and file-write.
 
+        .. deprecated:: v1.5
+            This method is deprecated in v1.5 and will be removed in v1.6.
+            Please call `training_type_plugin.save_checkpoint` directly.
+
         Args:
             checkpoint: dict containing model and trainer state
             filepath: write-target file's path
         """
+        rank_zero_deprecation(
+            "`Accelerator.save_checkpoint` is deprecated in v1.5 and will be removed in v1.6. "
+            "`save_checkpoint` logic is implemented directly in the `TrainingTypePlugin` implementations."
+        )
         self.training_type_plugin.save_checkpoint(checkpoint, filepath)
 
     @property
@@ -429,9 +532,17 @@ def setup_optimizers_in_pre_dispatch(self) -> bool:
         `TrainingTypePlugin` requires operating on the wrapped accelerator model. However this may break certain
         precision plugins such as APEX which require optimizers to be set.
 
+        .. deprecated:: v1.5
+            This property is deprecated in v1.5 and will be removed in v1.6.
+            Please call `training_type_plugin.setup_optimizers_in_pre_dispatch` directly.
+
         Returns:
             If True, delay setup optimizers until `pre_dispatch`, else call within `setup`.
         """
+        rank_zero_deprecation(
+            "`Accelerator.setup_optimizers_in_pre_dispatch` is deprecated in v1.5 and will be removed in v1.6. "
+            "Accesse `setup_optimizers_in_pre_dispatch directly` from the `TrainingTypePlugin`."
+        )
         return self.training_type_plugin.setup_optimizers_in_pre_dispatch
 
     @property
@@ -439,9 +550,17 @@ def restore_checkpoint_after_pre_dispatch(self) -> bool:
         """Override to delay restoring from checkpoint till after pre-dispatch. This is useful when the plugin
         requires all the setup hooks to run before loading checkpoint.
 
+        .. deprecated:: v1.5
+            This property is deprecated in v1.5 and will be removed in v1.6.
+            Please call `training_type_plugin.restore_checkpoint_after_pre_dispatch` directly.
+
         Returns:
             If true, restore checkpoint after pre_dispatch.
         """
+        rank_zero_deprecation(
+            "`Accelerator.restore_checkpoint_after_pre_dispatch` is deprecated in v1.5 and will be removed in v1.6. "
+            "Accesse `restore_checkpoint_after_pre_dispatch` directly from the `TrainingTypePlugin`."
+        )
         return self.training_type_plugin.restore_checkpoint_after_pre_dispatch
 
     def get_device_stats(self, device: Union[str, torch.device]) -> Dict[str, Any]:
@@ -460,34 +579,122 @@ def on_train_start(self) -> None:
         return self.training_type_plugin.on_train_start()
 
     def on_validation_start(self) -> None:
-        """Called when validation begins."""
+        """Called when validation begins.
+
+        See deprecation warning below.
+
+        .. deprecated:: v1.5
+            This method is deprecated in v1.5 and will be removed in v1.6.
+            Please call `training_type_plugin.on_validation_start` directly.
+        """
+        rank_zero_deprecation(
+            "`Accelerator.on_validation_start` is deprecated in v1.5 and will be removed in v1.6. "
+            "`on_validation_start` logic is implemented directly in the `TrainingTypePlugin` implementations."
+        )
         return self.training_type_plugin.on_validation_start()
 
     def on_test_start(self) -> None:
-        """Called when test begins."""
+        """Called when test begins.
+
+        See deprecation warning below.
+
+        .. deprecated:: v1.5
+            This method is deprecated in v1.5 and will be removed in v1.6.
+            Please call `training_type_plugin.on_test_start` directly.
+        """
+        rank_zero_deprecation(
+            "`Accelerator.on_test_start` is deprecated in v1.5 and will be removed in v1.6. "
+            "`on_test_start` logic is implemented directly in the `TrainingTypePlugin` implementations."
+        )
         return self.training_type_plugin.on_test_start()
 
     def on_predict_start(self) -> None:
-        """Called when predict begins."""
+        """Called when predict begins.
+
+        See deprecation warning below.
+
+        .. deprecated:: v1.5
+            This method is deprecated in v1.5 and will be removed in v1.6.
+            Please call `training_type_plugin.on_predict_start` directly.
+        """
+        rank_zero_deprecation(
+            "`Accelerator.on_predict_start` is deprecated in v1.5 and will be removed in v1.6. "
+            "`on_predict_start` logic is implemented directly in the `TrainingTypePlugin` implementations."
+        )
         return self.training_type_plugin.on_predict_start()
 
     def on_validation_end(self) -> None:
-        """Called when validation ends."""
+        """Called when validation ends.
+
+        See deprecation warning below.
+
+        .. deprecated:: v1.5
+            This method is deprecated in v1.5 and will be removed in v1.6.
+            Please call `training_type_plugin.on_validation_end` directly.
+        """
+        rank_zero_deprecation(
+            "`Accelerator.on_validation_end` is deprecated in v1.5 and will be removed in v1.6. "
+            "`on_validation_end` logic is implemented directly in the `TrainingTypePlugin` implementations."
+        )
         return self.training_type_plugin.on_validation_end()
 
     def on_test_end(self) -> None:
-        """Called when test end."""
+        """Called when test end.
+
+        See deprecation warning below.
+
+        .. deprecated:: v1.5
+            This method is deprecated in v1.5 and will be removed in v1.6.
+            Please call `training_type_plugin.on_test_end` directly.
+        """
+        rank_zero_deprecation(
+            "`Accelerator.on_test_end` is deprecated in v1.5 and will be removed in v1.6. "
+            "`on_test_end` logic is implemented directly in the `TrainingTypePlugin` implementations."
+        )
         return self.training_type_plugin.on_test_end()
 
     def on_predict_end(self) -> None:
-        """Called when predict ends."""
+        """Called when predict ends.
+
+        See deprecation warning below.
+
+        .. deprecated:: v1.5
+            This method is deprecated in v1.5 and will be removed in v1.6.
+            Please call `training_type_plugin.on_predict_end` directly.
+        """
+        rank_zero_deprecation(
+            "`Accelerator.on_predict_end` is deprecated in v1.5 and will be removed in v1.6. "
+            "`on_predict_end` logic is implemented directly in the `TrainingTypePlugin` implementations."
+        )
         return self.training_type_plugin.on_predict_end()
 
     def on_train_end(self) -> None:
-        """Called when train ends."""
+        """Called when train ends.
+
+        See deprecation warning below.
+
+        .. deprecated:: v1.5
+            This method is deprecated in v1.5 and will be removed in v1.6.
+            Please call `training_type_plugin.on_train_end` directly.
+        """
+        rank_zero_deprecation(
+            "`Accelerator.on_train_end` is deprecated in v1.5 and will be removed in v1.6. "
+            "`on_train_end` logic is implemented directly in the `TrainingTypePlugin` implementations."
+        )
         return self.training_type_plugin.on_train_end()
 
     # TODO: Update this in v1.7 (deprecation: #9816)
     def on_train_batch_start(self, batch: Any, batch_idx: int, dataloader_idx: int = 0) -> None:
-        """Called in the training loop before anything happens for that batch."""
+        """Called in the training loop before anything happens for that batch.
+
+        See deprecation warning below.
+
+        .. deprecated:: v1.5
+            This method is deprecated in v1.5 and will be removed in v1.6.
+            Please call `training_type_plugin.on_train_batch_start` directly.
+        """
+        rank_zero_deprecation(
+            "`Accelerator.on_train_batch_start` is deprecated in v1.5 and will be removed in v1.6. "
+            "`on_train_batch_start` logic is implemented directly in the `TrainingTypePlugin` implementations."
+        )
         return self.training_type_plugin.on_train_batch_start(batch, batch_idx)
diff --git a/pytorch_lightning/loops/dataloader/evaluation_loop.py b/pytorch_lightning/loops/dataloader/evaluation_loop.py
index 92c7d36cfd0d8..119e7f6c5472c 100644
--- a/pytorch_lightning/loops/dataloader/evaluation_loop.py
+++ b/pytorch_lightning/loops/dataloader/evaluation_loop.py
@@ -100,7 +100,7 @@ def advance(self, *args: Any, **kwargs: Any) -> None:
         void(*args, **kwargs)
 
         dataloader_idx: int = self.current_dataloader_idx
-        dataloader = self.trainer.accelerator.process_dataloader(self.current_dataloader)
+        dataloader = self.trainer.training_type_plugin.process_dataloader(self.current_dataloader)
         dataloader = self.trainer.data_connector.get_profiled_dataloader(dataloader, dataloader_idx=dataloader_idx)
         dl_max_batches = self._max_batches[dataloader_idx]
 
diff --git a/pytorch_lightning/loops/dataloader/prediction_loop.py b/pytorch_lightning/loops/dataloader/prediction_loop.py
index d4a6ab6d29cef..cf40316312107 100644
--- a/pytorch_lightning/loops/dataloader/prediction_loop.py
+++ b/pytorch_lightning/loops/dataloader/prediction_loop.py
@@ -84,7 +84,7 @@ def on_run_start(self) -> None:
     def advance(self, *args: Any, **kwargs: Any) -> None:
         """Predicts one entire dataloader."""
         void(*args, **kwargs)
-        dataloader = self.trainer.accelerator.process_dataloader(self.current_dataloader)
+        dataloader = self.trainer.training_type_plugin.process_dataloader(self.current_dataloader)
         dataloader_iter = enumerate(dataloader)
         dl_max_batches = self.max_batches[self.current_dataloader_idx]
 
diff --git a/pytorch_lightning/loops/fit_loop.py b/pytorch_lightning/loops/fit_loop.py
index 0d16c978fb374..6c692bb2dc6eb 100644
--- a/pytorch_lightning/loops/fit_loop.py
+++ b/pytorch_lightning/loops/fit_loop.py
@@ -204,7 +204,7 @@ def on_advance_start(self) -> None:
 
     def advance(self) -> None:
         """Runs one whole epoch."""
-        dataloader = self.trainer.accelerator.process_dataloader(self.trainer.train_dataloader)
+        dataloader = self.trainer.training_type_plugin.process_dataloader(self.trainer.train_dataloader)
         data_fetcher = self.trainer.data_connector.get_profiled_dataloader(dataloader)
 
         with self.trainer.profiler.profile("run_training_epoch"):
@@ -234,7 +234,7 @@ def on_run_end(self) -> None:
         self.trainer.call_hook("on_train_end")
 
         # give accelerators a chance to finish
-        self.trainer.accelerator.on_train_end()
+        self.trainer.training_type_plugin.on_train_end()
 
     def teardown(self) -> None:
         self.epoch_loop.teardown()
diff --git a/pytorch_lightning/loops/optimization/manual_loop.py b/pytorch_lightning/loops/optimization/manual_loop.py
index 21ad8738ab5bb..4c8bf157d331b 100644
--- a/pytorch_lightning/loops/optimization/manual_loop.py
+++ b/pytorch_lightning/loops/optimization/manual_loop.py
@@ -107,7 +107,7 @@ def advance(self, batch: Any, batch_idx: int) -> None:  # type: ignore[override]
             lightning_module._current_fx_name = "training_step"
             with self.trainer.profiler.profile("training_step"):
                 training_step_output = self.trainer.accelerator.training_step(step_kwargs)
-                self.trainer.accelerator.post_training_step()
+                self.trainer.training_type_plugin.post_training_step()
 
             del step_kwargs
 
diff --git a/pytorch_lightning/loops/optimization/optimizer_loop.py b/pytorch_lightning/loops/optimization/optimizer_loop.py
index 3a73795014c80..4ad85cc4650f2 100644
--- a/pytorch_lightning/loops/optimization/optimizer_loop.py
+++ b/pytorch_lightning/loops/optimization/optimizer_loop.py
@@ -450,7 +450,7 @@ def _training_step(self, split_batch: Any, batch_idx: int, opt_idx: int) -> Clos
             lightning_module._current_fx_name = "training_step"
             with self.trainer.profiler.profile("training_step"):
                 training_step_output = self.trainer.accelerator.training_step(step_kwargs)
-                self.trainer.accelerator.post_training_step()
+                self.trainer.training_type_plugin.post_training_step()
 
             del step_kwargs
 
diff --git a/pytorch_lightning/trainer/connectors/checkpoint_connector.py b/pytorch_lightning/trainer/connectors/checkpoint_connector.py
index d48ab3f518443..da6a81e8add44 100644
--- a/pytorch_lightning/trainer/connectors/checkpoint_connector.py
+++ b/pytorch_lightning/trainer/connectors/checkpoint_connector.py
@@ -465,7 +465,7 @@ def save_checkpoint(self, filepath: _PATH, weights_only: bool = False) -> None:
             weights_only: saving model weights only
         """
         _checkpoint = self.dump_checkpoint(weights_only)
-        self.trainer.accelerator.save_checkpoint(_checkpoint, filepath)
+        self.trainer.training_type_plugin.save_checkpoint(_checkpoint, filepath)
 
     def _get_lightning_module_state_dict(self) -> Dict[str, torch.Tensor]:
         metrics = (
@@ -478,7 +478,7 @@ def _get_lightning_module_state_dict(self) -> Dict[str, torch.Tensor]:
             metric.persistent(True)
             metric.sync()
 
-        state_dict = self.trainer.accelerator.lightning_module_state_dict()
+        state_dict = self.trainer.training_type_plugin.lightning_module_state_dict()
 
         for metric in metrics:
             # sync can be a no-op (e.g. on cpu) so `unsync` would raise a user error exception if we don't check
diff --git a/pytorch_lightning/trainer/trainer.py b/pytorch_lightning/trainer/trainer.py
index 01acae35fd46c..610f512324b82 100644
--- a/pytorch_lightning/trainer/trainer.py
+++ b/pytorch_lightning/trainer/trainer.py
@@ -1020,13 +1020,13 @@ def _run(self, model: "pl.LightningModule") -> Optional[Union[_EVALUATE_OUTPUT,
         self.callback_connector.attach_model_logging_functions(model)
 
         # attach model to the training type plugin
-        self.accelerator.connect(model)
+        self.training_type_plugin.connect(model)
 
         # hook
         self.data_connector.prepare_data()
         self.callback_connector._attach_model_callbacks()
 
-        if self._ckpt_path and not self.accelerator.restore_checkpoint_after_pre_dispatch:
+        if self._ckpt_path and not self.training_type_plugin.restore_checkpoint_after_pre_dispatch:
             self._load_checkpoint_weights()
 
         # ----------------------------
@@ -1037,7 +1037,7 @@ def _run(self, model: "pl.LightningModule") -> Optional[Union[_EVALUATE_OUTPUT,
         self._call_setup_hook()  # allow user to setup lightning_module in accelerator environment
 
         # check if we should delay restoring checkpoint till later
-        if not self.accelerator.restore_checkpoint_after_pre_dispatch:
+        if not self.training_type_plugin.restore_checkpoint_after_pre_dispatch:
             self.checkpoint_connector.resume_start()
             self._restore_modules_and_callbacks()
 
@@ -1055,9 +1055,9 @@ def _run(self, model: "pl.LightningModule") -> Optional[Union[_EVALUATE_OUTPUT,
                                 |                             ||
                          {self._dispatch}                     ||
                                 |                             ||  LIGHTNING
-                  {self.accelerator.start_training}           ||
-                or {self.accelerator.start_evaluating}        ||
-                or {self.accelerator.start_predicting}        ||  FLOW
+         {self.training_type_plugin.start_training}           ||
+       or {self.training_type_plugin.start_evaluating}        ||
+       or {self.training_type_plugin.start_predicting}        ||  FLOW
                                 |                             ||
                          {self.run_stage}                     ||
                                 |                             ||  DIRECTION
@@ -1087,7 +1087,7 @@ def _run(self, model: "pl.LightningModule") -> Optional[Union[_EVALUATE_OUTPUT,
         # plugin will setup fitting (e.g. ddp will launch child processes)
         self._pre_dispatch()
 
-        if self.accelerator.restore_checkpoint_after_pre_dispatch:
+        if self.training_type_plugin.restore_checkpoint_after_pre_dispatch:
             if self._ckpt_path:
                 self._load_checkpoint_weights()
 
@@ -1119,7 +1119,7 @@ def _run(self, model: "pl.LightningModule") -> Optional[Union[_EVALUATE_OUTPUT,
             self.state.status = TrainerStatus.FINISHED
         self.state.stage = None
 
-        return self.accelerator.results
+        return self.training_type_plugin.results
 
     def _pre_dispatch(self):
         self.accelerator.pre_dispatch(self)
@@ -1173,11 +1173,11 @@ def _post_dispatch(self):
 
     def _dispatch(self):
         if self.evaluating:
-            self.accelerator.start_evaluating(self)
+            self.training_type_plugin.start_evaluating(self)
         elif self.predicting:
-            self.accelerator.start_predicting(self)
+            self.training_type_plugin.start_predicting(self)
         else:
-            self.accelerator.start_training(self)
+            self.training_type_plugin.start_training(self)
 
     def run_stage(self):
         self.accelerator.dispatch(self)
@@ -1509,22 +1509,26 @@ def precision_plugin(self) -> PrecisionPlugin:
 
     @property
     def global_rank(self) -> int:
-        return self.accelerator.training_type_plugin.global_rank
+        return self.training_type_plugin.global_rank
 
     @property
     def local_rank(self) -> int:
         # some training types define a local rank
-        return getattr(self.accelerator.training_type_plugin, "local_rank", 0)
+        return getattr(self.training_type_plugin, "local_rank", 0)
 
     @property
     def node_rank(self) -> int:
         # some training types define a local rank
-        return getattr(self.accelerator.training_type_plugin, "node_rank", 0)
+        return getattr(self.training_type_plugin, "node_rank", 0)
 
     @property
     def world_size(self) -> int:
         # some training types define a world size
-        return getattr(self.accelerator.training_type_plugin, "world_size", 1)
+        return getattr(self.training_type_plugin, "world_size", 1)
+
+    @property
+    def should_rank_save_checkpoint(self) -> bool:
+        return self.training_type_plugin.should_rank_save_checkpoint
 
     @property
     def _distrib_type(self) -> DistributedType:
diff --git a/tests/accelerators/test_cpu.py b/tests/accelerators/test_cpu.py
index f95d182f9e5e1..697fae1644b1b 100644
--- a/tests/accelerators/test_cpu.py
+++ b/tests/accelerators/test_cpu.py
@@ -43,7 +43,7 @@ def test_restore_checkpoint_after_pre_dispatch_default():
     """Assert default for restore_checkpoint_after_pre_dispatch is False."""
     plugin = SingleDevicePlugin(torch.device("cpu"))
     accelerator = CPUAccelerator(training_type_plugin=plugin, precision_plugin=PrecisionPlugin())
-    assert not accelerator.restore_checkpoint_after_pre_dispatch
+    assert not accelerator.training_type_plugin.restore_checkpoint_after_pre_dispatch
     assert not plugin.restore_checkpoint_after_pre_dispatch
 
 
@@ -77,7 +77,7 @@ def load_checkpoint(self, checkpoint_path: Union[str, Path]) -> Dict[str, Any]:
     plugin = TestPlugin(torch.device("cpu"), checkpoint_io=TorchCheckpointIO())
     accelerator = CPUAccelerator(training_type_plugin=plugin, precision_plugin=PrecisionPlugin())
 
-    assert accelerator.restore_checkpoint_after_pre_dispatch == restore_after_pre_dispatch
+    assert accelerator.training_type_plugin.restore_checkpoint_after_pre_dispatch == restore_after_pre_dispatch
     assert plugin.restore_checkpoint_after_pre_dispatch == restore_after_pre_dispatch
 
     trainer = Trainer(
diff --git a/tests/deprecated_api/test_remove_1-6.py b/tests/deprecated_api/test_remove_1-6.py
index 546b25a54aa83..a5101d3311bf3 100644
--- a/tests/deprecated_api/test_remove_1-6.py
+++ b/tests/deprecated_api/test_remove_1-6.py
@@ -330,7 +330,7 @@ def test_v1_6_0_deprecated_device_dtype_mixin_import():
         from pytorch_lightning.utilities.device_dtype_mixin import DeviceDtypeModuleMixin  # noqa: F401
 
 
-def test_v1_6_0_deprecated_accelerator_collective():
+def test_v1_6_0_deprecated_accelerator_pass_through_functions():
     from pytorch_lightning.plugins.precision import PrecisionPlugin
     from pytorch_lightning.plugins.training_type import SingleDevicePlugin
 
@@ -347,3 +347,62 @@ def test_v1_6_0_deprecated_accelerator_collective():
     with pytest.deprecated_call(match="will be removed in v1.6"):
         tensor = torch.rand(2, 2, requires_grad=True)
         accelerator.all_gather(tensor)
+
+    with pytest.deprecated_call(match="will be removed in v1.6"):
+        model = BoringModel()
+        accelerator.connect(model)
+
+    with pytest.deprecated_call(match="will be removed in v1.6"):
+        accelerator.post_training_step()
+
+    with pytest.deprecated_call(match="will be removed in v1.6"):
+        tensor = torch.rand(2, 2, requires_grad=True)
+        accelerator.training_step_end(tensor)
+
+    with pytest.deprecated_call(match="will be removed in v1.6"):
+        tensor = torch.rand(2, 2, requires_grad=True)
+        accelerator.test_step_end(tensor)
+
+    with pytest.deprecated_call(match="will be removed in v1.6"):
+        tensor = torch.rand(2, 2, requires_grad=True)
+        accelerator.validation_step_end(tensor)
+
+    with pytest.deprecated_call(match="will be removed in v1.6"):
+        accelerator.lightning_module_state_dict()
+
+    with pytest.deprecated_call(match="will be removed in v1.6"):
+        dl = model.train_dataloader()
+        accelerator.process_dataloader(dl)
+
+    with pytest.deprecated_call(match="will be removed in v1.6"):
+        accelerator.results
+
+    with pytest.deprecated_call(match="will be removed in v1.6"):
+        accelerator.setup_optimizers_in_pre_dispatch
+
+    with pytest.deprecated_call(match="will be removed in v1.6"):
+        accelerator.restore_checkpoint_after_pre_dispatch
+
+    with pytest.deprecated_call(match="will be removed in v1.6"):
+        accelerator.on_validation_start()
+
+    with pytest.deprecated_call(match="will be removed in v1.6"):
+        accelerator.on_test_start()
+
+    with pytest.deprecated_call(match="will be removed in v1.6"):
+        accelerator.on_predict_start()
+
+    with pytest.deprecated_call(match="will be removed in v1.6"):
+        accelerator.on_validation_end()
+
+    with pytest.deprecated_call(match="will be removed in v1.6"):
+        accelerator.on_test_end()
+
+    with pytest.deprecated_call(match="will be removed in v1.6"):
+        accelerator.on_predict_end()
+
+    with pytest.deprecated_call(match="will be removed in v1.6"):
+        accelerator.on_train_end()
+
+    with pytest.deprecated_call(match="will be removed in v1.6"):
+        accelerator.on_train_batch_start(batch=None, batch_idx=0)
diff --git a/tests/plugins/test_ddp_fully_sharded_with_full_state_dict.py b/tests/plugins/test_ddp_fully_sharded_with_full_state_dict.py
index 61688b8847778..332c4e8d69d60 100644
--- a/tests/plugins/test_ddp_fully_sharded_with_full_state_dict.py
+++ b/tests/plugins/test_ddp_fully_sharded_with_full_state_dict.py
@@ -120,7 +120,7 @@ def test_fully_sharded_plugin_checkpoint_multi_gpus(tmpdir):
 
 def _assert_save_equality(trainer, ckpt_path, cls=TestFSDPModel):
     # Use FullySharded to get the state dict for the sake of comparison
-    model_state_dict = trainer.accelerator.lightning_module_state_dict()
+    model_state_dict = trainer.training_type_plugin.lightning_module_state_dict()
 
     if trainer.is_global_zero:
         saved_model = cls.load_from_checkpoint(ckpt_path)
diff --git a/tests/plugins/test_ddp_plugin.py b/tests/plugins/test_ddp_plugin.py
index 03cc0e1ff7beb..6c75a12e76bfc 100644
--- a/tests/plugins/test_ddp_plugin.py
+++ b/tests/plugins/test_ddp_plugin.py
@@ -108,7 +108,7 @@ def test_ddp_configure_ddp():
     )
     # test wrap the model if fitting
     trainer.state.fn = TrainerFn.FITTING
-    trainer.accelerator.connect(model)
+    trainer.training_type_plugin.connect(model)
     trainer.accelerator.setup_environment()
     trainer.accelerator.setup(trainer)
     trainer.lightning_module.trainer = trainer
@@ -122,7 +122,7 @@ def test_ddp_configure_ddp():
         plugins=[ddp_plugin],
     )
     # test do not wrap the model if trainerFN is not fitting
-    trainer.accelerator.connect(model)
+    trainer.training_type_plugin.connect(model)
     trainer.accelerator.setup_environment()
     trainer.accelerator.setup(trainer)
     trainer.lightning_module.trainer = trainer