diff --git a/airflow-core/src/airflow/jobs/scheduler_job_runner.py b/airflow-core/src/airflow/jobs/scheduler_job_runner.py
index f093a3e360776..981117c073339 100644
--- a/airflow-core/src/airflow/jobs/scheduler_job_runner.py
+++ b/airflow-core/src/airflow/jobs/scheduler_job_runner.py
@@ -283,7 +283,8 @@ def register_signals(self) -> ExitStack:
 
     def _exit_gracefully(self, signum: int, frame: FrameType | None) -> None:
         """Clean up processor_agent to avoid leaving orphan processes."""
-        self._end_active_spans()
+        if self._is_tracing_enabled():
+            self._end_active_spans()
 
         if not _is_parent_process():
             # Only the parent process should perform the cleanup.
@@ -1931,7 +1932,8 @@ def _schedule_dag_run(
                 return callback
 
             if (
-                dag_run.scheduled_by_job_id is not None
+                self._is_tracing_enabled()
+                and dag_run.scheduled_by_job_id is not None
                 and dag_run.scheduled_by_job_id != self.job.id
                 and self.active_spans.get(dag_run.run_id) is None
             ):