diff --git a/x-pack/plugin/security/src/main/java/org/elasticsearch/xpack/security/authz/store/NativePrivilegeStore.java b/x-pack/plugin/security/src/main/java/org/elasticsearch/xpack/security/authz/store/NativePrivilegeStore.java
index 8aea63dc34b36..45cd8de8ac974 100644
--- a/x-pack/plugin/security/src/main/java/org/elasticsearch/xpack/security/authz/store/NativePrivilegeStore.java
+++ b/x-pack/plugin/security/src/main/java/org/elasticsearch/xpack/security/authz/store/NativePrivilegeStore.java
@@ -177,12 +177,13 @@ private QueryBuilder getApplicationNameQuery(Collection<String> applications) {
         }
         final BoolQueryBuilder boolQuery = QueryBuilders.boolQuery();
         if (termsQuery != null) {
-            boolQuery.filter(termsQuery);
+            boolQuery.should(termsQuery);
         }
         for (String wildcard : wildcardNames) {
             final String prefix = wildcard.substring(0, wildcard.length() - 1);
-            boolQuery.filter(QueryBuilders.prefixQuery(APPLICATION.getPreferredName(), prefix));
+            boolQuery.should(QueryBuilders.prefixQuery(APPLICATION.getPreferredName(), prefix));
         }
+        boolQuery.minimumShouldMatch(1);
         return boolQuery;
     }
 
diff --git a/x-pack/plugin/security/src/test/java/org/elasticsearch/xpack/security/authz/store/NativePrivilegeStoreTests.java b/x-pack/plugin/security/src/test/java/org/elasticsearch/xpack/security/authz/store/NativePrivilegeStoreTests.java
index 657a1f47e42d9..b1daf77d395fe 100644
--- a/x-pack/plugin/security/src/test/java/org/elasticsearch/xpack/security/authz/store/NativePrivilegeStoreTests.java
+++ b/x-pack/plugin/security/src/test/java/org/elasticsearch/xpack/security/authz/store/NativePrivilegeStoreTests.java
@@ -189,7 +189,7 @@ public void testGetPrivilegesByWildcardApplicationName() throws Exception {
         assertThat(request.indices(), arrayContaining(RestrictedIndicesNames.SECURITY_MAIN_ALIAS));
 
         final String query = Strings.toString(request.source().query());
-        assertThat(query, containsString("{\"bool\":{\"filter\":[{\"terms\":{\"application\":[\"yourapp\"]"));
+        assertThat(query, containsString("{\"bool\":{\"should\":[{\"terms\":{\"application\":[\"yourapp\"]"));
         assertThat(query, containsString("{\"prefix\":{\"application\":{\"value\":\"myapp-\""));
         assertThat(query, containsString("{\"term\":{\"type\":{\"value\":\"application-privilege\""));
 
diff --git a/x-pack/plugin/src/test/resources/rest-api-spec/test/privileges/20_has_application_privs.yml b/x-pack/plugin/src/test/resources/rest-api-spec/test/privileges/20_has_application_privs.yml
index eb92cc252b560..b23862c5553da 100644
--- a/x-pack/plugin/src/test/resources/rest-api-spec/test/privileges/20_has_application_privs.yml
+++ b/x-pack/plugin/src/test/resources/rest-api-spec/test/privileges/20_has_application_privs.yml
@@ -109,6 +109,27 @@ setup:
               ]
             }
 
+  - do:
+      security.put_role:
+        name: "role_containing_wildcard_app_name_and_plain_app_name"
+        body:  >
+          {
+            "cluster": [],
+            "indices": [],
+            "applications": [
+              {
+                "application": "myapp",
+                "privileges": ["user"],
+                "resources": ["*"]
+              },
+              {
+                "application": "yourapp-*",
+                "privileges": ["read"],
+                "resources": ["*"]
+              }
+            ]
+          }
+
   # And a user for each role
   - do:
       security.put_user:
@@ -134,6 +155,14 @@ setup:
                 "password": "p@ssw0rd",
                 "roles" : [ "yourapp_read_config" ]
               }
+  - do:
+      security.put_user:
+        username: "myapp_yourapp_wildard_role_user"
+        body:  >
+          {
+            "password": "p@ssw0rd",
+            "roles" : [ "role_containing_wildcard_app_name_and_plain_app_name" ]
+          }
 
 ---
 teardown:
@@ -168,6 +197,11 @@ teardown:
         username: "your_read"
         ignore: 404
 
+  - do:
+      security.delete_user:
+        username: "myapp_yourapp_wildard_role_user"
+        ignore: 404
+
   - do:
       security.delete_role:
         name: "myapp_engineering_read"
@@ -182,6 +216,12 @@ teardown:
       security.delete_role:
         name: "yourapp_read_config"
         ignore: 404
+
+  - do:
+      security.delete_role:
+        name: "role_containing_wildcard_app_name_and_plain_app_name"
+        ignore: 404
+
 ---
 "Test has_privileges with application-privileges":
   - do:
@@ -291,3 +331,48 @@ teardown:
         }
       }
     } }
+
+  - do:
+      headers: { Authorization: "Basic bXlhcHBfeW91cmFwcF93aWxkYXJkX3JvbGVfdXNlcjpwQHNzdzByZA==" } # myapp_yourapp_wildard_role_user
+      security.has_privileges:
+        user: null
+        body: >
+          {
+            "application": [
+              {
+                "application" : "myapp",
+                "resources" : [ "*" ],
+                "privileges" : [ "action:login" ]
+              },
+              {
+                "application" : "yourapp-v1",
+                "resources" : [ "*" ],
+                "privileges" : [ "read" ]
+              },
+              {
+                "application" : "yourapp-v2",
+                "resources" : [ "*" ],
+                "privileges" : [ "read" ]
+              }
+            ]
+          }
+
+  - match: { "username" : "myapp_yourapp_wildard_role_user" }
+  - match: { "has_all_requested" : true }
+  - match: { "application" : {
+    "myapp" : {
+      "*" : {
+        "action:login" : true
+      }
+    },
+    "yourapp-v1": {
+      "*": {
+        "read": true
+      }
+    },
+    "yourapp-v2": {
+      "*": {
+        "read": true
+      }
+    }
+  } }