Mixed duke's port for a game (4,5)
I believe the answer is:
stud poker
'game' is the definition.
(I know that stud poker is a type of poker)
'mixed duke's port' is the wordplay.
'mixed' indicates anagramming the letters.
'dukes'+'port'='dukesport'
'dukesport' with letters rearranged gives 'STUD POKER'.
'for a' is the link.
(Other definitions for stud poker that I've seen before include "Variation of five-card gambling game" , "Gambling game with some cards turned face up" , "It involves dealer" , "Card gambling game -- Turk's dope (anag)" .)