Trainer has month to improve, all concluding (4)
I believe the answer is:
shoe
'trainer' is the definition.
(I've seen this before)
'has month to improve all concluding' is the wordplay.
'all concluding' indicates one should take the final letters.
The last letters of 'has month to improve' are 'SHOE'.
(Other definitions for shoe that I've seen before include "Hose for the foot?" , "Work as a farrier" , "Case from which playing cards are delt one at a time" , "this goes about a foot" , "Maybe casual" .)