He has a chance of winning in the last round (8)
I believe the answer is:
finalist
'he has a chance' is the definition.
The answer is a person as well as being a singular noun. This is suggested by the definition.
'winning in the last round' is the wordplay.
'winning' becomes 'fi' (I can't justify this - if you can you should believe this answer much more).
'round' indicates anagramming the letters.
'in'+'last'='inlast'
'inlast' is an anagram of 'nalist'.
'fi'+'nalist'='FINALIST'
'of' is the link.
Can you help me to learn more?
(Other definitions for finalist that I've seen before include "Competitor who has beaten all except one" , "Winner of semi-final" , "No more rounds for me!" , "possible winner" , "One reaching last match" .)