The last one to appear in home game (5)
I believe the answer is:
omega
'the last' is the definition.
(thesaurus)
'one to appear in home game' is the wordplay.
'one to appear in' indicates a hidden word (I've seen 'appearing in' mean this).
'OMEGA' can be found hidden inside 'home game'.
(Other definitions for omega that I've seen before include "symbol of resistance?" , "Traditional story" , "Greek long 'o'" , "End of sequence" , "The last in a series of letters" .)