Politician cycling for nation with luck (5)

I believe the answer is:

irish

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'politician' is the definition.
The definition and answer can be both people as well as being singular nouns.
Perhaps they are linked in a way I don't understand?

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

Can you help me to learn more?

(Other definitions for irish that I've seen before include "Hibernian -- breed of 4" , "Hi, Sir, ar you a Celt?" , "From Galway, say" , "Nationality" , "From Eire" .)

I've seen this clue in The Independent.

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