Carol is smart wasting little time (4)
I believe the answer is:
sing
'carol' is the definition.
(carol can mean to sing carols)
'smart wasting little time' is the wordplay.
'smart' becomes 'sting' (both can mean to burn or hurt).
'wasting' is a deletion indicator.
'little time' becomes 't' (abbreviation for time).
'sting' with 't' removed is 'SING'.
'is' acts as a link.
(Other definitions for sing that I've seen before include "Chorus" , "Croon" , "pipe" , "behave like noisy tits" , "Perform (a song)" .)