Deter daughter getting publicity in publication (8)
I believe the answer is:
dissuade
'deter' is the definition.
('dissuade' can be a synonym of 'deter')
'daughter getting publicity in publication' is the wordplay.
'daughter' becomes 'd'.
'getting' means one lot of letters go next to another.
'publicity' becomes 'ad' (advert).
'in' is an insertion indicator.
'publication' becomes 'issue' ('issue' can be a synonym of 'publication'**).
'ad' inserted inside 'issue' is 'issuade'.
'd'+'issuade'='DISSUADE'
(Other definitions for dissuade that I've seen before include "Persuade not to" , "Advise not to proceed" , "Discourage from course of action" , "Deter by advice" , "Put off" .)