Go on irritating Republican joint (6)
I believe the answer is:
rankle
'go on irritating' is the definition.
(I've seen this before)
'republican joint' is the wordplay.
'republican' becomes 'r' (abbreviation).
'joint' becomes 'ankle' (ankle is a kind of joint).
'r'+'ankle'='RANKLE'
(Other definitions for rankle that I've seen before include "Cause lasting bitterness and resentment" , "Chafe" , "Eat into and cause resentment" , "Continually vex or irritate" , "Continue vexing" .)