Putting me in goal is correct (5)
I believe the answer is:
emend
'is correct' is the definition.
(to emend something is to correct or improve it)
'putting me in goal' is the wordplay.
I cannot really see how this works, but
'me' is present in the answer.
'goal' could be 'end' (both can mean a purpose) and 'end' is found within the answer.
No letters remain.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for emend that I've seen before include "Edit; make alterations to a draft" , "do editorial work" , "Alter something written to correct errors" , "Make correction in written material" , "get rid of faults" .)