In the final bit this writer is improving (8)
I believe the answer is:
emending
'improving' is the definition.
(emending is a kind of improving)
'in the final bit this writer' is the wordplay.
'in the' indicates putting letters inside.
'final bit' becomes 'ending'.
'this writer' becomes 'me' (the person who is writing these clues).
'ending' enclosing 'me' is 'EMENDING'.
'is' acts as a link.
(Other definitions for emending that I've seen before include "Removing errors and making improvements" , "Setting right, correcting" , "... putting things right" .)