Study, once more, the publicity (4)
I believe the answer is:
read
'study' is the definition.
(I know that study can be written as read)
'once more the publicity' is the wordplay.
'once more' becomes 're' (prefix in words like 're-emerge' or 're-enter').
'the publicity' becomes 'ad' (short for advert).
're'+'ad'='READ'
(Other definitions for read that I've seen before include "register" , "Study (subject at university)" , "Interpreted, for example" , "Comprehend written words" , "See - peruse - understand" .)