Extremist is awful cad, liar (7)
I believe the answer is:
radical
'extremist' is the definition.
(I know that extremist can be written as radical)
'awful cad liar' is the wordplay.
'awful' indicates anagramming the letters.
'cad'+'liar'='cadliar'
'cadliar' with letters rearranged gives 'RADICAL'.
'is' acts as a link.
(Other definitions for radical that I've seen before include "Deep-seated" , "Thoroughgoing - (popularly) extremist" , "Holding extreme political views" , "Complete" , "Drastic or thorough as changes may be" .)