Aristocrat but not of the French game (5)
I believe the answer is:
chess
'game' is the definition.
(board game)
'aristocrat but not of the french' is the wordplay.
'aristocrat' becomes 'duchess' (duchess is a type of aristocrat).
'but not' suggests deleting specific letters.
'of the french' becomes 'du' ('of the' in French).
'duchess' with 'du' taken out is 'CHESS'.
(Other definitions for chess that I've seen before include "Musical - board game" , "Board game for two players" , "show" , "Sixteen-men-a-side game" , "Pure-skill board game" .)