Not a person that fails to finish in time (4)
I believe the answer is:
noon
'time' is the definition.
(I know that noon is a type of hour)
'not a person that fails to finish' is the wordplay.
'not a person' becomes 'no-one' (I've seen this before).
'that fails to finish' means to remove the last letter.
'noone' with its last letter taken off is 'NOON'.
'in' acts as a link.
(Other definitions for noon that I've seen before include "Twelve o'clock, midday" , "[LUNCHTIME] ?" , "See 8" , "High time of day?" , "Twelve during daylight" .)