Stop publicity happening (7)
I believe the answer is:
prevent
'stop' is the definition.
(thesaurus)
'publicity happening' is the wordplay.
'publicity' becomes 'pr'.
'happening' becomes 'event' (I've seen this before).
'pr'+'event'='PREVENT'
(Other definitions for prevent that I've seen before include "Thwart" , "Bar" , "Stop, hinder" , "Avert, hinder" , "Keep from happening" .)