Alimony's first cut admitting mean payment (9)
I believe the answer is:
allowance
'payment' is the definition.
(allowance is a kind of payment)
'alimony's first cut admitting mean' is the wordplay.
'first' indicates taking the first letters.
'cut' becomes 'lance' (I've seen this before).
'admitting' is an insertion indicator (admit can mean to welcome in or accept).
'mean' becomes 'low' (both can mean nasty or dishonourable).
The initial letter of 'alimonys' is 'a'.
'lance' placed around 'low' is 'llowance'.
'a'+'llowance'='ALLOWANCE'
(Other definitions for allowance that I've seen before include "Ocean wall (anag.)" , "Ration, quota" , "An amount granted for a period" , "Money granted for a purpose" , "Money for agreed expenses" .)