Girl admits publicity dodge (5)
I believe the answer is:
evade
'dodge' is the definition.
('evade' can be a synonym of 'dodge')
'girl admits publicity' is the wordplay.
'girl' becomes 'eve' (**).
'admits' is an insertion indicator.
'publicity' becomes 'ad' (advert).
'eve' going around 'ad' is 'EVADE'.
(Other definitions for evade that I've seen before include "Fail to pay" , "Shun, escape" , "Escape (something)" , "Dodge, keep clear of" , "avoid answering" .)