Finished _not out”, but exhausted (4,2)
I believe the answer is:
done in
'exhausted' is the definition.
(I've seen this in another clue)
'finished not out' is the wordplay.
'finished' becomes 'done' (both can mean completed).
'not out' becomes 'in' ('in' is the opposite to 'out').
'done'+'in'='DONE IN'
'but' is the link.
(Other definitions for done in that I've seen before include "Spent" , "whacked" , "Wasted" , "lacking strength" , "very tired" .)