Card game in British newspaper (4)
I believe the answer is:
brag
'card game' is the definition.
(brag is an old card game)
'british newspaper' is the wordplay.
'british' becomes 'b' (abbreviation e.g. in 'BBC').
'newspaper' becomes 'rag' (informal term for a newspaper).
'b'+'rag'='BRAG'
'in' acts as a link.
(Other definitions for brag that I've seen before include "'Show off, boast (4)'" , "Blow one's own trumpet" , "Shoot a line" , "boast; form of poker" , "Talk boastfully" .)