Study a book about publicity (4)
I believe the answer is:
read
'study a book' is the definition.
'read' can be an answer for 'study' (synonyms). I'm not certain of the 'a book' bit.
'about publicity' is the wordplay.
'about' becomes 're' ('re' means regarding or about).
'publicity' becomes 'ad' (short for advert).
're'+'ad'='READ'
Can you help me to learn more?
(Other definitions for read that I've seen before include "Stomach" , "register" , "(Of passage) have a certain wording" , "what follows 18 [OMASUM] in a 17 [RUMINANT]" , "Looked at and understood" .)