Stern about editor that’s set up proof-corrector (6)
I believe the answer is:
reader
'proof-corrector' is the definition.
(I've seen this before)
'stern about editor that's set up' is the wordplay.
'stern' becomes 'rear' ('rear' can be a synonym of 'stern').
'about' means one lot of letters goes inside another.
'editor' becomes 'ed'.
'that's set up' is a reversal indicator.
'ed' written backwards gives 'de'.
'rear' enclosing 'de' is 'READER'.
(Other definitions for reader that I've seen before include "Times subscriber, perhaps?" , "Person addressed by author" , "She lectures" , "Reared by book lover" , "Person perusing a book or newspaper" .)