One needing floor that's hard and carpet free? (3,6)

I believe the answer is:

tap dancer

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'one needing floor that's hard' is the definition.
The answer is a person as well as being a singular noun. This is suggested by the definition.

'and carpet free?' is the wordplay.
'free?' indicates anagramming the letters (I've seen 'freed' mean this).
'and'+'carpet'='andcarpet'
'andcarpet' anagrammed gives 'TAP-DANCER'.

Can you help me to learn more?

(Other definitions for tap dancer that I've seen before include "Performer good on wooden stage" , "Heel and toe clicker?" , "Entertainer needing floorboards" , "Hard shoe entertainer" , "Astaire or Kelly, for example" .)

I've seen this clue in The Times.

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