breathe down someone's neck(за кем-либо: The supervisor is always breathing down the necks of the employees – Надзиратель всегда внимательно наблюдает за служащимиTaras)
keep a sharp eye on(It seems that vandals marking their names or other messages on the rock don't get to appreciate their names for long; city staffers keep a sharp eye on the famous landmark, and the instant anyone soils its pristine whiteness, it is immediately repainted. (Chuck Davis)ART Vancouver)