Love playing game to the end (5)
I believe the answer is:
omega
'the end' is the definition.
(last letter of the Greek alphabet)
'love playing game' is the wordplay.
'love' becomes 'o' (love means zero in tennis).
'playing' indicates anagramming the letters.
'game' is an anagram of 'mega'.
'o'+'mega'='OMEGA'
'to' acts as a link.
(Other definitions for omega that I've seen before include "16 letter" , "24th Greek letter" , "The last in a series of letters" , "Art of story-telling by body movement" , "in Greece, the limit!" .)