President in cycling event (7)

I believe the answer is:

madison

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

I don't understand how the rest of the clue works.

Can you help me to learn more?

(Other definitions for madison that I've seen before include "US President and Avenue" , "NY avenue associated with the advertising industry" , "United States president -- Wisconsin's capital" , "State capital of Wisconsin" , "James -, fourth president of the USA" .)

I've seen this clue in The Daily Express.

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