Old Bill, firm yet soft (3)

I believe the answer is:

cop

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'old bill' is the definition.
(I know that old bill can be written as cop)

'firm yet soft' is the wordplay.
'firm' becomes 'co' (a firm is a company).
'yet soft' becomes 'p' (musical abbreviation for 'piano'. I am not sure about the 'yet' bit.).
'co'+'p'='COP'

Can you help me to learn more?

(Other definitions for cop that I've seen before include "Police officer (informal)" , "Policeman (slang)" , "catch" , "Policeman (colloq.)" , "Policeman (informal)" .)

I've seen this clue in the Evening Standard.

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