Root for extremist (7)
I believe the answer is:
radical
This clue is a double definition.
'root' is the first definition.
('radical' can be a synonym of 'root')
'extremist' is the second definition.
('radical' can be a synonym of 'extremist')
'for' is the link.
(Other definitions for radical that I've seen before include "Going to the roots, fundamental as change may be" , "Innovative, progressive" , "Militant" , "'Revolutionary, extremist (7)'" , "Progressive - car dial (anag)" .)