Supervise, keep an eye on (7)
I believe the answer is:
oversee
I believe this clue is a double definition.
'supervise' is the first definition.
(synonyms)
'keep an eye on' is the second definition.
(to oversee is to watch over)
(Other definitions for oversee that I've seen before include "Watch people toil" , "Exercise supervision" , "Act as tutor" , "Inspect" , "What superintendent will do" .)