breathe a sigh of relief
US /briːð ə saɪ əv rɪˈliːf/
UK /briːð ə saɪ əv rɪˈliːf/

1.
to feel relieved after a period of anxiety or worry
:
•
She breathed a sigh of relief when she heard her son was safe.
•
We all breathed a sigh of relief when the plane landed safely.