Holding extreme political views (7)
I believe the answer is:
radical
'holding extreme political views' is the definition.
(I've seen this before)
This is the entire clue.
(Other definitions for radical that I've seen before include "Progressive - car dial (anag)" , "Drastic and thorough, as reforms may be" , "Deep-seated" , "Innovative, progressive" , "left-winger" .)