diff --git a/CHANGELOG.md b/CHANGELOG.md
index d9cab7a63eca6..1d7573af02513 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -177,7 +177,9 @@ The format is based on [Keep a Changelog](http://keepachangelog.com/en/1.0.0/).
 
 ### Fixed
 
-- Set better defaults for `rank_zero_only.rank` when training is launched with SLURM and torchelastic ([#6802](https://github.com/PyTorchLightning/pytorch-lightning/pull/6802/))
+- Set better defaults for `rank_zero_only.rank` when training is launched with SLURM and torchelastic:
+    * Support SLURM and torchelastic global rank environment variables ([#5715](https://github.com/PyTorchLightning/pytorch-lightning/pull/5715))
+    * Remove hardcoding of local rank in accelerator connector ([#6878](https://github.com/PyTorchLightning/pytorch-lightning/pull/6878))
 
 
 - Sanitize `None` params during pruning ([#6836](https://github.com/PyTorchLightning/pytorch-lightning/pull/6836))
diff --git a/pytorch_lightning/trainer/connectors/accelerator_connector.py b/pytorch_lightning/trainer/connectors/accelerator_connector.py
index 1e00d33cdf05a..aa52ec1c40d82 100644
--- a/pytorch_lightning/trainer/connectors/accelerator_connector.py
+++ b/pytorch_lightning/trainer/connectors/accelerator_connector.py
@@ -59,7 +59,6 @@
     device_parser,
     DeviceType,
     DistributedType,
-    rank_zero_only,
 )
 from pytorch_lightning.utilities.distributed import rank_zero_info, rank_zero_warn
 from pytorch_lightning.utilities.exceptions import MisconfigurationException
@@ -112,12 +111,6 @@ def __init__(
         self._training_type_plugin: Optional[TrainingTypePlugin] = None
         self._cluster_environment: Optional[ClusterEnvironment] = None
 
-        # init the default rank if exists
-        # we need to call this here or NVIDIA flags and other messaging in init will show on all ranks
-        # this way we only show it on rank 0
-        if "LOCAL_RANK" in os.environ:
-            rank_zero_only.rank = int(os.environ["LOCAL_RANK"])
-
         # for gpus allow int, string and gpu list
         if auto_select_gpus and isinstance(gpus, int):
             self.gpus = pick_multiple_gpus(gpus)