Game fellow finally greeting saint (5)
I believe the answer is:
whist
'game' is the definition.
(I know that whist is a card game)
'fellow finally greeting saint' is the wordplay.
'finally' suggests the final letters.
'greeting' becomes 'hi' (hi is a kind of greeting).
'saint' becomes 'st' (abbreviation).
The last letter of 'fellow' is 'w'.
'w'+'hi'+'st'='WHIST'
(Other definitions for whist that I've seen before include "Card game, often played at a "drive"" , "Demand silence" , "18th-century card game, the forerunner of bridge" , "Popular card game, sometimes solo" , "Card-game" .)