Finish with this writer in editing (8)
I believe the answer is:
emending
'editing' is the definition.
(to emend something is to edit it)
'finish with this writer' is the wordplay.
'finish' becomes 'ending' (I've seen this before).
'with' indicates putting letters inside.
'this writer' becomes 'me' (the person who is writing these clues).
'ending' enclosing 'me' is 'EMENDING'.
'in' is the link.
(Other definitions for emending that I've seen before include "... putting things right" , "Removing errors and making improvements" , "Setting right, correcting" .)