Boast made by British tabloid? (4)
I believe the answer is:
brag
'boast' is the definition.
(I know that boast can be written as brag)
'by british tabloid?' is the wordplay.
'by' says to put letters next to each other.
'british' becomes 'b' (abbreviation e.g. in BBC).
'tabloid?' becomes 'rag' (informal term for a tabloid newspaper).
'b'+'rag' is 'BRAG'.
'made' is the link.
(Other definitions for brag that I've seen before include "boast; form of poker" , "popular with 15 [EGOTIST] , no doubt" , "game, making > boast" , "Boast, crow" , "Card game, like poker" .)