First of games, a home win (4)
I believe the answer is:
gain
'win' is the definition.
('gain' can be a synonym of 'win')
'first of games a home' is the wordplay.
'first of' suggests taking the first letters.
'home' becomes 'in' ('he's home' can mean 'he's in').
The initial letter of 'games' is 'g'.
'g'+'a'+'in'='GAIN'
(Other definitions for gain that I've seen before include "Pick up" , "Advance" , "Win" , "Obtain, secure" , "Obtain; earn" .)