In conclusion, this writer's correct (5)
I believe the answer is:
emend
'correct' is the definition.
(I've seen this before)
'in conclusion this writer's' is the wordplay.
'in' is an insertion indicator.
'conclusion' becomes 'end' (something's conclusion is its end).
'this writer' becomes 'me' (the setter of the puzzle is the writer of the clue).
'end' placed around 'me' is 'EMEND'.
(Other definitions for emend that I've seen before include "Improve by editing" , "Remove faults from" , "would appear better" , "Improve (texts)" , "Improve by altering" .)