The craze for noisy publicity? (3)
I believe the answer is:
fad
'the craze' is the definition.
(synonyms)
'noisy publicity?' is the wordplay.
'noisy' becomes 'f'.
'publicity?' becomes 'ad' (advert).
'f'+'ad'='FAD'
'for' acts as a link.
(Other definitions for fad that I've seen before include "A craze or current vogue" , "Caprice" , "A passing fashion or craze" , "Craze; idiosyncrasy" , "A passing liking or fashion" .)