Don't go on about me to improve matters (5)
I believe the answer is:
emend
'improve matters' is the definition.
'emend' can be an answer for 'improve' (emending is a kind of improving). I am unsure of the 'matters' bit.
'don't go on about me' is the wordplay.
'don't go on' becomes 'end' (I can't explain this - if you can you should give a lot more credence to this answer).
'about' is an insertion indicator.
'end' enclosing 'me' is 'EMEND'.
'to' acts as a link.
Can you help me to learn more?
(Other definitions for emend that I've seen before include "Remove errors" , "change" , "Alter something written to correct errors" , "Polish" , "make an improvement" .)