Polish in game with British (3)
I believe the answer is:
rub
'polish' is the definition.
(polish meaning rub to make shiny)
'game with british' is the wordplay.
'game' becomes 'RU' (rugby union).
'with' is a charade indicator (letters next to each other).
'british' becomes 'b' (abbreviation e.g. in 'BBC').
'ru'+'b'='RUB'
'in' is the link.
(Other definitions for rub that I've seen before include "Remove marks - ... out" , "Chafe; difficulty" , "Polish - difficulty" , "Polish or massage" , "Cause friction" .)