keep a low profile
US /kiːp ə loʊ ˈproʊ.faɪl/
UK /kiːp ə loʊ ˈproʊ.faɪl/

1.
to avoid attracting attention or publicity
:
•
After the scandal, he decided to keep a low profile for a while.
•
The celebrity tried to keep a low profile while on vacation.