Cut back primarily on game (4)
I believe the answer is:
polo
'game' is the definition.
(polo is a kind of game)
'cut back primarily on' is the wordplay.
'cut' becomes 'lop' (lopping is a kind of cutting**).
'back' says the letters should be written backwards.
'primarily' says to take the initial letters.
The first letter of 'on' is 'o'.
'lop' written backwards gives 'pol'.
'pol'+'o'='POLO'
(Other definitions for polo that I've seen before include "What riders might get up to in a team" , "Sport - mint - explorer" , "Venetian 19 to Asia, servant to Kublai Khan" , "Equestrian game" , "jersey" .)