Quick to criticise papers (5)
I believe the answer is:
rapid
'quick' is the definition.
('rapid' can be a synonym of 'quick')
'criticise papers' is the wordplay.
'criticise' becomes 'rap' (I've seen this before).
'papers' becomes 'id' (identification papers).
'rap'+'id'='RAPID'
'to' acts as a link.
(Other definitions for rapid that I've seen before include "moving fast" , "Quickly accomplished" , "Quick or swift" , "Electrical connector" , "Happening quickly" .)