Hangman, say, backing American profligate (9)
I believe the answer is:
suspender
'hangman say' is the definition.
'backing american profligate' is the wordplay.
'backing' is a reversal indicator.
'american' becomes 'us'.
'profligate' becomes 'spender' (spender is a kind of profligate).
'us' back-to-front is 'su'.
'su'+'spender'='SUSPENDER'
(Other definitions for suspender that I've seen before include "One responsible for hold-up" , "hanger on?" , "hangman?" , "Sock support" , "Supporter" .)