Snapped, about to sleep (3)
I believe the answer is:
nap
'sleep' is the definition.
(a nap is a short sleep)
'snapped about' is the wordplay.
'about' indicates a hidden word (the clue goes around or about the answer).
'NAP' is hidden in the letters of 'snapped'.
'to' acts as a link.
(Other definitions for nap that I've seen before include "Short sleep on fuzzy fabric surface" , "Raised fibres on surface of cloth or leather" , "Kip" , "Racing tip that professes to be a certainty" , "Racing tip that claims to be a certainty" .)