Quite mean to trap Republican (6)
I believe the answer is:
pretty
'quite' is the definition.
(synonyms)
'mean to trap republican' is the wordplay.
'mean' becomes 'petty' (I've seen this in another clue).
'to trap' is an insertion indicator.
'republican' becomes 'r' (abbreviation).
'petty' going around 'r' is 'PRETTY'.
(Other definitions for pretty that I've seen before include "Attractive in delicate way" , "Fairly - good-looking" , "Pleasing to look at" , "Attractive - quite" , "Pleasing on the eye" .)