Crossword Genius

Bishop hosting a series of bike races has a quiet pedal (3-4)

Ross

I believe the answer is:

rat-trap

I'm a little stuck... Click here to teach me more about this clue!

'pedal' is the definition.
(I've seen this before)

'bishop hosting a series of bike races has a quiet' is the wordplay.
I cannot really see how this works, but
'a' is within the answer.
'races' could be 'tt' (Isle of Man Tourist Trophy races) and 'tt' is located in the answer.
'bishop' could be 'rr' (abbreviation for Right Reverend) and 'rr' is found in the leftover letters.
'quiet' could be 'p' (music symbol for 'piano', ie soft or quiet) and 'p' is present in the answer.
A single letter 'a' remains which might be clued in a way I don't see.
This may be the basis of the clue (or it may be nonsense).

Can you help me to learn more?

(Other definitions for rat-trap that I've seen before include "Rodent catcher - found on a bicycle!" , "Means of catching rodent" .)

I've seen this clue in The Times.
Want a hint initially instead of a full solution? Install my app