diff --git a/jupyter_client/tests/test_utils.py b/jupyter_client/tests/test_utils.py
new file mode 100644
index 000000000..dd6849192
--- /dev/null
+++ b/jupyter_client/tests/test_utils.py
@@ -0,0 +1,30 @@
+import asyncio
+from unittest import mock
+
+import pytest
+
+from jupyter_client.utils import run_sync
+
+
+@pytest.fixture
+def loop():
+    loop = asyncio.new_event_loop()
+    asyncio.set_event_loop(loop)
+    return loop
+
+
+def test_run_sync_clean_up_task(loop):
+    async def coro_never_called():
+        pytest.fail("The call to this coroutine is not expected")
+
+    # Ensure that run_sync cancels the pending task
+    with mock.patch.object(loop, "run_until_complete") as patched_loop:
+        patched_loop.side_effect = KeyboardInterrupt
+        with mock.patch("asyncio.ensure_future") as patched_ensure_future:
+            mock_future = mock.Mock()
+            patched_ensure_future.return_value = mock_future
+            with pytest.raises(KeyboardInterrupt):
+                run_sync(coro_never_called)()
+            mock_future.cancel.assert_called_once()
+            # Suppress 'coroutine ... was never awaited' warning
+            patched_ensure_future.call_args[0][0].close()