Correct from the first person up to the last (5)
I believe the answer is:
emend
'correct' is the definition.
(thesaurus)
'the first person up to the last' is the wordplay.
'the first person' becomes 'me' (first-person pronoun).
'up' says the letters should be written in reverse (in down clue: letters go upwards).
'to the last' becomes 'end'.
'me' written backwards gives 'em'.
'em'+'end'='EMEND'
'from' acts as a link.
(Other definitions for emend that I've seen before include "get rid of faults" , "Edit, improve" , "Correct and improve the text" , "Modify" , "make an improvement" .)