Golfer upset about a putt at first in game (8)
I believe the answer is:
leapfrog
'game' is the definition.
(leapfrog is a kind of game)
'golfer upset about a putt at first' is the wordplay.
'upset' indicates anagramming the letters.
'about' is an insertion indicator.
'at first' suggests taking the first letters.
The first letter of 'putt' is 'p'.
'golfer' anagrammed gives 'lefrog'.
'a'+'p'='ap'
'lefrog' enclosing 'ap' is 'LEAPFROG'.
'in' acts as a link.
(Other definitions for leapfrog that I've seen before include "Advance by jumping over the opposition" , "bound over" , "Overtake in position" , "Children's game of jumping over each other" , "Advance by jumps" .)