Publicity provided by some mouthy peer (4)
I believe the answer is:
hype
'publicity' is the definition.
(hype is a kind of publicity)
'some mouthy peer' is the wordplay.
'some' indicates a hidden word (some of the parts of the word are used).
'HYPE' can be found hidden inside 'mouthy peer'.
'provided by' acts as a link.
(Other definitions for hype that I've seen before include "Overdo promotion" , "Slang for extravagant promotion of a product" , "Promotional publicity" , "Plug" , "Artificially induced excitement" .)