Tidies up the refuge without bristles (11)

I believe the answer is:

cleanshaven

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'without bristles' is the definition.
I don't know anything about this answer so I can't tell whether this works.

'tidies up the refuge' is the wordplay.
'tidies up' becomes 'cleans' (cleaning is a kind of tidying up).
'the refuge' becomes 'haven' (I've seen this in another clue).
'cleans'+'haven'='CLEANSHAVEN'

Can you help me to learn more?

I've seen this clue in the Sydney Morning Herald.

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