He finishes off the game with hesitation (6)
I believe the answer is:
killer
'he finishes' is the definition.
The answer is a person as well as being a singular noun. This is suggested by the definition.
'off the game with hesitation' is the wordplay.
I cannot quite understand how this works, but
'off' could be 'kill' ('off' can informally mean 'murder') and 'kill' is found within the answer.
'hesitation' could be 'er' (sound used when hesitating) and 'er' is found in the answer.
No letters remain.
This may be the basis of the clue (or it may be nonsense).
Can you help me to learn more?
(Other definitions for killer that I've seen before include "One murdering" , "Slaughterer" , "Slayer" , "stupendous!" , "really impressive" .)