Publicity is about over for this handsome youth (6)
I believe the answer is:
adonis
'this handsome youth' is the definition.
(I've seen this before)
'publicity is about over' is the wordplay.
'publicity' becomes 'ad' (advert).
'about' becomes 'on' (**).
'over' means one lot of letters go next to another.
'is' put after 'on' is 'onis'.
'ad'+'onis'='ADONIS'
'for' is the link.
(Other definitions for adonis that I've seen before include "Handsome youth - said no (anag)" , "Handsome fellow" , "In Greek myth, handsome youth beloved of Aphrodite" , "No aids (anag)" , "Legendary lover" .)