Not quite twelve -- sleep lightly (4)
I believe the answer is:
doze
'sleep lightly' is the definition.
(I've seen this in another clue)
'not quite twelve' is the wordplay.
'not quite' means to remove the last letter.
'twelve' becomes 'dozen' (synonyms).
'dozen' with its final letter removed is 'DOZE'.
(Other definitions for doze that I've seen before include "Catnap" , "Take nap" , "little sleep" , "Snooze" , "A short light sleep" .)