Not late, but almost not beginning (5)
I believe the answer is:
early
'not late' is the definition.
('early' is the opposite to 'late')
'almost not beginning' is the wordplay.
'almost' becomes 'nearly' (synonyms).
'not beginning' means to remove the first letter.
'nearly' with its initial letter taken off is 'EARLY'.
'but' acts as a link.
(Other definitions for early that I've seen before include "Gothic style following 13" , "Untimely" , "Post this for Christmas?" , "Ahead of schedule" , "before anyone else?" .)