Correct only after bit of publicity (6)
I believe the answer is:
adjust
'correct' is the definition.
(adjusting is a kind of correcting)
'only after bit of publicity' is the wordplay.
I cannot quite understand how this works, but
'only' could be 'just' (synonyms) and 'just' is found in the answer.
'publicity' could be 'ad' (short for advert) and 'ad' is present in the answer.
This accounts for all the letters.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for adjust that I've seen before include "suit" , "Arrange, put into proper position" , "Change slightly to fit" , "Adapt (to new situation)" , "Make slight corrections to" .)