diff --git a/dvc/repo/experiments/gc.py b/dvc/repo/experiments/gc.py
index b33d40b41..3dfeade22 100644
--- a/dvc/repo/experiments/gc.py
+++ b/dvc/repo/experiments/gc.py
@@ -3,6 +3,7 @@ from typing import Optional
 
 from dvc.repo import locked
 
+from .base import EXEC_APPLY, EXEC_BRANCH, EXEC_CHECKPOINT
 from .utils import exp_refs
 
 logger = logging.getLogger(__name__)
@@ -31,9 +32,20 @@ def gc(
     if not keep_revs:
         return 0
 
+    exec_branch = repo.scm.get_ref(EXEC_BRANCH, follow=False)
+    exec_apply = repo.scm.get_ref(EXEC_APPLY)
+    exec_checkpoint = repo.scm.get_ref(EXEC_CHECKPOINT)
+
     removed = 0
     for ref_info in exp_refs(repo.scm):
         if ref_info.baseline_sha not in keep_revs:
+            ref = repo.scm.get_ref(str(ref_info))
+            if exec_branch and str(ref_info):
+                repo.scm.remove_ref(EXEC_BRANCH)
+            if exec_apply and exec_apply == ref:
+                repo.scm.remove_ref(EXEC_APPLY)
+            if exec_checkpoint and exec_checkpoint == ref:
+                repo.scm.remove_ref(EXEC_CHECKPOINT)
             repo.scm.remove_ref(str(ref_info))
             removed += 1