Persevering figure is given account with financial promises (9)
I believe the answer is:
tenacious
'persevering' is the definition.
(I've seen this before)
'figure is given account with financial promises' is the wordplay.
'figure' becomes 'ten' (ten is a number or figure).
'is given' means one lot of letters go next to another.
'account' becomes 'ac' (abbreviation for account).
'with' is a charade indicator (letters next to each other).
'financial promises' becomes 'IOUs' (promises to pay a debt).
'ten'+'ac'+'ious'='TENACIOUS'
(Other definitions for tenacious that I've seen before include "Determined" , "Persevering" , "Holding fast" , "Persistent in holding on" , "Dogged" .)