Person who hates games teacher, last in contest (6)
I believe the answer is:
rabbit
'person who hates games' is the definition.
(person who is bad at sport)
'teacher last in contest' is the wordplay.
'teacher' becomes 'rabbi' (I've seen this before).
'last in' indicates one should take the final letters.
The last letter of 'contest' is 't'.
'rabbi'+'t'='RABBIT'
(Other definitions for rabbit that I've seen before include "Animal with hole" , "Burrow dweller" , "Bit bar (anag.)" , "Gas" , "Burrowing animal or rotten tennis player" .)