on the watch

on the watch (for someone or something)

Actively and attentively looking out for someone or something. You need to be on the watch for suspicious people when you're out in the city this late at night. A: "We've had reports of counterfeit products coming through the shipping yard." B: "Don't worry, I've already put extra inspectors on the watch."
See also: on, someone, watch
Farlex Dictionary of Idioms. © 2015 Farlex, Inc, all rights reserved.

on the watch (for someone or something)

alert and watching for someone or something. Please stay on the watch for trouble. I'm always on the watch for Ann. I want to know when she's around.
See also: on, watch
McGraw-Hill Dictionary of American Idioms and Phrasal Verbs. © 2002 by The McGraw-Hill Companies, Inc.
See also:
References in classic literature ?
He was afraid to try to go through his companion's pockets, however; and besides the cabbie might be on the watch. He had the hundred safe, and he would have to be content with that.