Runs British city (6)

I believe the answer is:

bleeds

'runs' is the definition.
('bleed' can be a synonym of 'run')

'british city' is the wordplay.
'british' becomes 'b' (abbreviation e.g. in BBC).
'city' becomes 'Leeds' (city in England).
'b'+'leeds'='BLEEDS'

(Another definition for bleeds that I've seen is " Loses blood".)

I've seen this clue in The Guardian.

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