Bluster of second-rate newspaper (4)
I believe the answer is:
brag
'bluster' is the definition.
('brag' can be a synonym of 'bluster')
'second-rate newspaper' is the wordplay.
'second rate' becomes 'b'.
'newspaper' becomes 'rag' (rag is a kind of newspaper).
'b'+'rag'='BRAG'
'of' acts as a link.
(Other definitions for brag that I've seen before include "Boast, exaggerate" , "Boast about garb" , "Boast, crow" , "game of bluff" , "Boast ? card-game" .)