Accept no garbage (6)

I believe the answer is:

refuse

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'garbage' is the definition.
('refuse' can be a synonym of 'garbage')

I don't understand how the rest of the clue works.

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(Other definitions for refuse that I've seen before include "Say no to - rubbish" , "Turn down - rubbish" , "Waste, garbage" , "Decline to accept - rubbish" , "deadwood" .)

I've seen this clue in the Evening Standard.

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