Deter daughter getting publicity in publication (8)
I believe the answer is:
Here is my best explanation:
'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'.
(Other definitions for dissuade that I've seen before include "Put off", "Discourage from course of action", "Persuade not to", "Advise not to proceed", "Deter by advice", "put off" and "Try to deter".)