Idiot, finishing sulkily, spoils reward for last place (5,5)
I believe the answer is:
booby prize
'reward for last place' is the definition.
(joke prize given to a loser)
'idiot finishing sulkily spoils' is the wordplay.
'idiot' becomes 'boob' (both can mean a stupid person).
'finishing' suggests the final letters (the letter which finishes the word).
'spoils' becomes 'prize' (both can mean a reward).
The last letter of 'sulkily' is 'y'.
'boob'+'y'+'prize'='BOOBY PRIZE'
(Other definitions for booby prize that I've seen before include "presentation that's made to last" , "Wooden spoon" .)