President's event in the velodrome (7)

I believe the answer is:

madison

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'president's' is the definition.
(James Madison, fourth president of the USA)

I can't explain the rest of the clue.

(Other definitions for madison that I've seen before include "United States president -- Wisconsin's capital" , "James -, fourth president of the USA" , "dance?" , "State capital of Wisconsin" , "James, fourth US president" .)

I've seen this clue in The Daily Express.

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