Crossword Genius

Clean up one's way of operating, on the quiet (3)

Ross

I believe the answer is:

mop

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

'clean up' is the definition.
(I've seen this in another clue)

'one's way of operating on the quiet' is the wordplay.
I cannot really understand how this works, but
'of' could be 'o' and 'o' is present in the answer.
'quiet' could be 'p' (music symbol for 'piano', ie soft or quiet) and 'p' is found in the answer.
A single letter 'm' 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 mop that I've seen before include "Hair, unkempt" , "Mass of disordered hair" , "Floor wiper" , "Finish off a task - . . . up" , "Cleaning implement" .)

I've seen this clue in the Evening Standard.
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