diff --git a/python_modules/dagster/dagster/_core/execution/plan/instance_concurrency_context.py b/python_modules/dagster/dagster/_core/execution/plan/instance_concurrency_context.py
index 3bc7f15982beb..2835582c3b647 100644
--- a/python_modules/dagster/dagster/_core/execution/plan/instance_concurrency_context.py
+++ b/python_modules/dagster/dagster/_core/execution/plan/instance_concurrency_context.py
@@ -13,6 +13,8 @@
 STEP_UP_BASE = 1.1
 MAX_CONCURRENCY_CLAIM_BLOCKED_INTERVAL = 15
 
+MAX_ALLOWED_PRIORITY = 2**31 - 1
+
 
 class InstanceConcurrencyContext:
     """This class is used to manage instance-scoped concurrency for a given run. It wraps the
@@ -57,8 +59,11 @@ def __exit__(
             to_clear.append(step_key)
 
         for step_key in to_clear:
-            del self._pending_timeouts[step_key]
-            del self._pending_claim_counts[step_key]
+            if step_key in self._pending_timeouts:
+                del self._pending_timeouts[step_key]
+            if step_key in self._pending_claim_counts:
+                del self._pending_claim_counts[step_key]
+
             self._pending_claims.remove(step_key)
 
         self._context_guard = False
@@ -105,6 +110,12 @@ def claim(self, concurrency_key: str, step_key: str, step_priority: int = 0):
             self._pending_claims.add(step_key)
 
         priority = self._run_priority + step_priority
+
+        if abs(priority) > MAX_ALLOWED_PRIORITY:
+            raise Exception(
+                f"Tried to claim a concurrency slot with a priority {priority} that was not in the allowed range of a 32-bit signed integer."
+            )
+
         claim_status = self._instance.event_log_storage.claim_concurrency_slot(
             concurrency_key, self._run_id, step_key, priority
         )
diff --git a/python_modules/dagster/dagster_tests/core_tests/execution_tests/test_instance_concurrency_context.py b/python_modules/dagster/dagster_tests/core_tests/execution_tests/test_instance_concurrency_context.py
index fce54b40889bc..65a8bc01da17f 100644
--- a/python_modules/dagster/dagster_tests/core_tests/execution_tests/test_instance_concurrency_context.py
+++ b/python_modules/dagster/dagster_tests/core_tests/execution_tests/test_instance_concurrency_context.py
@@ -292,3 +292,19 @@ def test_run_step_priority(concurrency_instance):
         time.sleep(0.1)
 
         assert low_context.claim("foo", "low_run_low_step", step_priority=-1)  # -1001
+
+        with pytest.raises(
+            Exception,
+            match="Tried to claim a concurrency slot with a priority -2147483648 that was not in the allowed range of a 32-bit signed integer.",
+        ):
+            low_context.claim("foo", "too_low_step", step_priority=-(2**31 - 1) + 1000 - 1)
+
+        low_context.claim("foo", "too_low_step", step_priority=-(2**31 - 1) + 1000)
+
+        with pytest.raises(
+            Exception,
+            match="Tried to claim a concurrency slot with a priority 2147483648 that was not in the allowed range of a 32-bit signed integer.",
+        ):
+            regular_context.claim("foo", "too_high_step", step_priority=(2**31 - 1) + 1)
+
+        regular_context.claim("foo", "too_high_step", step_priority=-(2**31 - 1))