Snapped, having little sleep (3)
I believe the answer is:
nap
'little sleep' is the definition.
(I've seen this before)
'snapped having' is the wordplay.
'having' indicates a hidden word.
'NAP' is hidden within 'snapped'.
(Other definitions for nap that I've seen before include "raised bits of velvet" , "Card game - quick sleep" , "A brief snooze" , "One likely to win" , "Sleep - card game - fibres on a snooker table" .)