Almost 12? Sleep (4)
I believe the answer is:
doze
'sleep' is the definition.
(thesaurus)
'almost 12?' is the wordplay.
'almost' means to remove the last letter (most of the word but not all of it).
'12?' becomes 'dozen' ('dozen' can be a synonym of '12').
'dozen' with its last letter taken away is 'DOZE'.
(Other definitions for doze that I've seen before include "Take nap" , "Go to sleep" , "Sleep fitfully" , "Snooze" , "Nod off" .)