Kick out former wife with occupation about sex (9)
I believe the answer is:
extradite
'kick out' is the definition.
(extraditing is a kind of kicking out)
'former wife with occupation about sex' is the wordplay.
'former wife' becomes 'ex'.
'with' means one lot of letters go next to another.
'occupation' becomes 'trade' (trade is a kind of occupation**).
'about' indicates putting letters inside.
'sex' becomes 'it' (a common euphemism).
'trade' going around 'it' is 'tradite'.
'ex'+'tradite'='EXTRADITE'
(Other definitions for extradite that I've seen before include "Hand over for trial to another jurisdiction" , "Banish" , "Send away for trial!" , "Hand over (felon) to another country" , "Hand over to authorities of another country" .)