Maybe thirty-one or over in game (7)
I believe the answer is:
primero
'game' is the definition.
(I have seen 'Old game' mean 'primero' so perhaps 'game' could also mean 'primero')
'maybe thirty-one or over' is the wordplay.
'maybe thirty one' becomes 'prime' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'over' shows that the letters should be reversed in order.
'or' in reverse letter order is 'ro'.
'prime'+'ro'='PRIMERO'
'in' acts as a link.
Can you help me to learn more?
(Another definition for primero that I've seen is " Old card game, rip more (anag.)".)