Chap short of time (3)
I believe the answer is:
tim
'chap' is the definition.
(short for Timothy)
'short of time' is the wordplay.
'short of' means to remove the last letter (I've seen 'short' mean this).
'time' with its final letter removed is 'TIM'.
(Other definitions for tim that I've seen before include "Tiny . . . is a lovable small boy from Dickens" , "Little fellow" , "Tiny ..., endearing Dickens boy" , "Tiny . . . is a loveable boy in fiction" , "Adjoin" .)