Either radical heads Conservative dissenter (7)
I believe the answer is:
heretic
'dissenter' is the definition.
(I know that heretic is a type of nonconformist)
'either radical heads conservative' is the wordplay.
'radical' indicates an anagram.
'heads' says to put letters next to each other (some letters go ahead of others).
'conservative' becomes 'c' (UK political abbreviation).
'either' is an anagram of 'hereti'.
'hereti'+'c'='HERETIC'
(Other definitions for heretic that I've seen before include "Etheric (anag.)" , "Religious outcast" , "One breaking with orthodox beliefs" , "One whose opinions are contrary to accepted religious beliefs" , "Nonconformist" .)