A mark in the foreign game
I believe the answer is:
la crosse
'game' is the definition.
(I've seen this before)
'a mark in the foreign' is the wordplay.
'mark' becomes 'cross' ('cross' can be a synonym of 'mark'**).
'in' is an insertion indicator.
'the foreign' becomes 'le' ('the' in French).
'a'+'cross'='across'
'across' going into 'le' is 'LA CROSSE'.
(Other definitions for la crosse that I've seen before include "Ball game using netted stick" , "Game with stick and net" , "Team sport" , "Team game with ball and sticks" , "Cor! seals can play this ball game" .)