Keep an eye on the timekeeper (5)
I believe the answer is:
watch
I believe this clue is a double definition.
'keep an eye on' is the first definition.
(synonyms)
'the timekeeper' is the second definition.
(watch is a kind of timekeeper)
(Other definitions for watch that I've seen before include "Keep under observation" , "Timepiece - look out" , "View" , "period of duty" , "Keep an eye on - timepiece" .)