Collar getting black: race to find cleaner (9)

I believe the answer is:

nailbrush

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'cleaner' is the definition.
(something which cleans nails)

'collar getting black race' is the wordplay.
'collar getting' becomes 'nail' (I can't explain this - if you can you should give a lot more credence to this answer).
'black' becomes 'b' (as in pencil classifications).
'race' becomes 'rush' (synonyms).
'nail'+'b'+'rush'='NAILBRUSH'

'to find' acts as a link.

Can you help me to learn more?

(Other definitions for nailbrush that I've seen before include "Item used in manicure" , "Use this to clean claws" , "Cleaning device" , "Shun Blair (anag)" , "Cleaner" .)

I've seen this clue in The Times.

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