Golfer and PA playing game (8)
I believe the answer is:
leapfrog
'game' is the definition.
(I know that leapfrog is a type of child\\u0027s game)
'golfer and pa playing' is the wordplay.
'and' is a charade indicator (letters next to each other).
'playing' indicates an anagram.
'golfer' put after 'pa' is 'pagolfer'.
'pagolfer' with letters rearranged gives 'LEAPFROG'.
(Other definitions for leapfrog that I've seen before include "Advance by jumping over the opposition" , "Vaulting game" , "Game in which players vault over each other" , "Overtake in position" , "Child's game of jumping over other children" .)