Not all catch up (4)
I believe the answer is:
part
'not all' is the definition.
('part' is the opposite to 'all')
'catch up' is the wordplay.
'catch' becomes 'trap' (trapping is a kind of catching).
'up' says the letters should be written in reverse (in down clue: letters go upwards).
'trap' written backwards gives 'PART'.
(Other definitions for part that I've seen before include "Region" , "unemployed actor hopes for" , "Piece; divide" , "Portion, segment" , "Piece, segment" .)