Bicycle Race is playing after Crazy (7)
I believe the answer is:
madison
'bicycle race' is the definition.
Although both the answer and definition are singular nouns, I cannot see how they can define each other.
'is playing after crazy' is the wordplay.
'playing' becomes 'on' (on can mean playing or performing).
'after' says to put letters next to each other.
'crazy' becomes 'mad' (synonyms).
'is'+'on'='ison'
'ison' put after 'mad' is 'MADISON'.
Can you help me to learn more?
(Other definitions for madison that I've seen before include "US president, county and square" , "US President - county with bridges" , "James, fourth US president" , "-- Avenue, New York's advertising district" , "New York Avenue for advertising people" .)