Snapped, having to sleep (3)
I believe the answer is:
nap
'sleep' is the definition.
(a nap is a short sleep)
'snapped having' is the wordplay.
'having' indicates the answer is hidden within the clue.
'NAP' can be found hidden inside 'snapped'.
'to' acts as a link.
(Other definitions for nap that I've seen before include "Kip" , "One likely to win" , "A daytime doze" , "Raised fibres on surface of cloth or leather" , "Racing tip that professes to be a certainty" .)