roving eye
Noun
Meaning
(idiomatic) Wide-ranging observation of one's surroundings.
(idiomatic) The personal characteristic of taking amorous interest in people other than one's own spouse or regular romantic partner.
Source: en.wiktionary.orgExamples
They successfully combined piracy and puritanism, which aren't so unlike when you come right down to it. Both had a strong dislike for opposition and both had a roving eye for other people's property.
The negligence of Nature wide and wild, Where, undisguised by mimic art, she spreads Unbounded beauty to the roving eye.