Endlessly aspire to put an end to game (9)
I believe the answer is:
hopscotch
'to game' is the definition.
(hopscotch is a kind of game)
'endlessly aspire to put an end' is the wordplay.
'endlessly' means to remove the last letter.
'aspire' becomes 'hope' (I've seen this in another clue).
'to put an end' becomes 'scotch' (I've seen this before).
'hope' with its final letter removed is 'hop'.
'hop'+'scotch'='HOPSCOTCH'
(Other definitions for hopscotch that I've seen before include "Traditional children's game" , "Children's pavement game" , "child's play" , "childish amusement" , "Jumping game" .)