Dirt Conservative's found in shoe (7)
I believe the answer is:
scandal
'dirt' is the definition.
(synonyms)
'conservative's found in shoe' is the wordplay.
'conservative' becomes 'C' (abbreviation commonly used in UK politics).
'found in' means one lot of letters goes inside another.
'shoe' becomes 'sandal' (sandal is a kind of shoe).
'c' inserted within 'sandal' is 'SCANDAL'.
(Other definitions for scandal that I've seen before include "Outraging event" , "Shocking disgrace" , "dirt" , "Dishonour" , "Shocking thing" .)