Almost time to sleep, but not quite (4)
I believe the answer is:
nigh
'not quite' is the definition.
(thesaurus)
'almost time to sleep' is the wordplay.
'almost' means to remove the last letter (most of the word but not all of it).
'time to sleep' becomes 'night' (I've seen this in another clue).
'night' with its last letter removed is 'NIGH'.
'but' acts as a link.
(Other definitions for nigh that I've seen before include "Near, as in archaic usage" , "Nearby" , "See 23" , "Near at hand" , "Near in time or place" .)