A good shot but not quite a winner (5)
I believe the answer is:
inner
'a good shot' is the definition.
(I've seen this before)
'not quite a winner' is the wordplay.
'not quite' means to remove the first letter.
'winner' with its initial letter removed is 'INNER'.
'but' is the link.
(Other definitions for inner that I've seen before include "red" , "Central area of a city, often old" , "Very private room" , "Relating to the soul, mind or spirit" , "Central, internal" .)