Final character to love playing game (5)
I believe the answer is:
omega
'final character' is the definition.
(last letter of the Greek alphabet)
'love playing game' is the wordplay.
'love' becomes 'o' (love means zero in tennis).
'playing' is an anagram indicator.
'game' is an anagram of 'mega'.
'o'+'mega'='OMEGA'
'to' is the link.
(Other definitions for omega that I've seen before include "Art of story-telling by body movement" , "Greek character symbolizing resistance" , "Final outcome" , "End of sequence" , "long letter" .)