Greek character featuring in home game (5)
I believe the answer is:
omega
'greek character' is the definition.
(letter from the Greek alphabet)
'in home game' is the wordplay.
'in' says the answer is hidden in the clue.
'OMEGA' is hidden within 'home game'.
'featuring' acts as a link.
(Other definitions for omega that I've seen before include "Traditional story" , "Ultimate letter" , "24th Greek letter" , "completes a series" , "The last in a series of letters" .)