Bike race that's foolhardy will go ahead (7)
I believe the answer is:
madison
'bike race' is the definition.
Although both the answer and definition are singular nouns, I don't understand how they can define each other.
'foolhardy will go ahead' is the wordplay.
I cannot quite see how this works, but
'ahead' could be 'on' (synonyms) and 'on' is found in the answer.
This may be the basis of the clue (or it may be nonsense).
'that's' acts as a link.
Can you help me to learn more?
(Other definitions for madison that I've seen before include "United States president -- Wisconsin's capital" , "State capital of Wisconsin" , "New York Avenue for advertising people" , "US president - New York square with gardens" , "NY avenue associated with the advertising industry" .)