have a roving eye
US /hæv ə ˈroʊvɪŋ aɪ/
UK /hæv ə ˈroʊvɪŋ aɪ/
1.
to be someone who is always looking at other people and is often unfaithful in a relationship
:
•
He can't be trusted; he always seems to have a roving eye.
•
Despite being married, he still has a roving eye.