At home following golf, strange game (3,5)
I believe the answer is:
gin rummy
'game' is the definition.
(card game)
'at home following golf strange' is the wordplay.
'at home' becomes 'in' ('I'm in' can mean 'I'm at home').
'following' means one lot of letters go next to another.
'golf' becomes 'g' (phonetic alphabet: alpha, bravo, charlie etc.).
'strange' becomes 'rummy' (similar in meaning).
'in' put after 'g' is 'gin'.
'gin'+'rummy'='GIN RUMMY'
(Other definitions for gin rummy that I've seen before include "Card game" , "cards" .)