Decline to admit a Conservative's in front (6)
I believe the answer is:
facade
'front' is the definition.
(I know that facade is a type of front)
'decline to admit a conservative's' is the wordplay.
'decline' becomes 'fade' (I've seen this before).
'to admit' indicates putting letters inside.
'conservative' becomes 'C' (UK political abbreviation).
'a'+'c'='ac'
'fade' placed around 'ac' is 'FACADE'.
'in' is the link.
(Other definitions for facade that I've seen before include "piece by Walton" , "exterior" , "Walton's setting of Sitwell's verses" , "Showy front" , "Front - mask" .)