Impudent youngster, Conservative success (4)
I believe the answer is:
chit
'impudent youngster' is the definition.
(I've seen this before)
'conservative success' is the wordplay.
'conservative' becomes 'C' (abbreviation commonly used in UK politics).
'success' becomes 'hit' (hit is a kind of success).
'c'+'hit'='CHIT'
(Other definitions for chit that I've seen before include "Official voucher" , "struck" , "Pert young lady" , "Short official note recording a sum owed" , "Informal receipt" .)