keep_an_eye_on
1. [ verb ] keep under careful scrutiny
Synonyms: look_after
Examples:

"Keep an eye on this prisoner!"

Related terms: watch
2. [ verb ] follow with the eyes or the mind
Synonyms: watch follow observe watch_over
Examples:

"Keep an eye on the baby, please!" "The world is watching Sarajevo" "She followed the men with the binoculars"

Related terms: check guard invigilate keep_tabs_on trace perceiver observation notice watch