Figure identified admitting affair ... (9)
I believe the answer is:
seventeen
'figure' is the definition.
(I've seen this before)
'identified admitting affair' is the wordplay.
'identified' becomes 'seen' (identify can mean to recognise or see).
'admitting' means one lot of letters goes inside another (admit can mean to welcome in or accept).
'affair' becomes 'event' (I've seen this before).
'seen' going around 'event' is 'SEVENTEEN'.
(Other definitions for seventeen that I've seen before include "Age when full driving licence can be obtained" , "next clue" , "odd number" , "Quite a few" , "Figure" .)