Study once again the publicity (4)
I believe the answer is:
read
'study' is the definition.
(I know that study can be written as read)
'again the publicity' is the wordplay.
'again' becomes 're' (prefix meaning 'again').
'the publicity' becomes 'ad' (short for advert).
're'+'ad'='READ'
'once' is the link.
(Other definitions for read that I've seen before include "examined" , "what follows 18 [OMASUM] in a 17 [RUMINANT]" , "Lecture" , "Perused" , "Comprehend written words" .)