Aristocrats expected by society to embrace the mating game (9)
I believe the answer is:
duchesses
'aristocrats' is the definition.
(duchess is a kind of aristocrat)
'expected by society to embrace the mating game' is the wordplay.
'expected' becomes 'due' (similar in meaning).
'by' means one lot of letters go next to another.
'society' becomes 's' (common abbreviation in names of organisations).
'to embrace' indicates putting letters inside.
'the mating game' becomes 'chess' (as in checkmate).
'due'+'s'='dues'
'dues' enclosing 'chess' is 'DUCHESSES'.
(Other definitions for duchesses that I've seen before include "ladies" , "aristocrats" .)