First to score home goal, making comeback for game (6)
I believe the answer is:
tennis
'game' is the definition.
(tennis is a kind of game)
'first to score home goal making comeback' is the wordplay.
'first to' indicates taking the first letters.
'home' becomes 'in' ('he's home' can mean 'he's in').
'goal' becomes 'net' (net is a kind of goal).
'making comeback' says the letters should be written in reverse.
The initial letter of 'score' is 's'.
's'+'in'+'net'='sinnet'
'sinnet' in reverse letter order is 'TENNIS'.
'for' is the link.
(Other definitions for tennis that I've seen before include "Game that depends on service" , "Real or lawn game" , "Sport Dwight Davis gave trophy for" , "Game (where love is nought?)" , "Sport on a court" .)