Idiot in Conservative group (4)
I believe the answer is:
clot
'idiot' is the definition.
(both can mean a stupid person)
'conservative group' is the wordplay.
'conservative' becomes 'C' (UK political abbreviation).
'group' becomes 'lot' ().
'c'+'lot'='CLOT'
'in' is the link.
(Other definitions for clot that I've seen before include "Semi-solid mass -- dunce" , "Fool - congeal" , "(Of blood) coagulate" , "3 [DUMMY]" , "Thrombus - fool" .)