Bill's constant success (4)
I believe the answer is:
chit
'bill's' is the definition.
(chit is a kind of bill)
'constant success' is the wordplay.
'constant' becomes 'c' (mathematical abbreviation).
'success' becomes 'hit' (hit is a kind of success).
'c'+'hit'='CHIT'
(Other definitions for chit that I've seen before include "Impudent girl" , "Receipt; a child" , "Official voucher" , "bill to pay" , "Brief note" .)