Home game includes last in a series (5)
I believe the answer is:
omega
'last in a series' is the definition.
(I've seen this before)
'home game includes' is the wordplay.
'includes' indicates the answer is hidden within the clue.
'OMEGA' is hidden in the letters of 'home game'.
(Other definitions for omega that I've seen before include "in Greece, the limit!" , "Last (Gk. letter)" , "Greek character symbolizing resistance" , "24th Greek letter" , "Greek finalist" .)