Verb
keep a close watch (third-person singular simple present keeps a close watch, present participle keeping a close watch, simple past and past participle kept a close watch)
(idiomatic) to pay careful attention to a situation or a thing, so that you can deal with any changes or problems.
The prime minister asked the home secretary to keep a close watch on the flooding situation.
I keep a close watch on this heart of mine; I keep my eyes wide open all the time. I keep the ends out for the tie that binds. Because you're mine, I walk the line. Johnny Cash