Who hangs a brace? (9)

I believe the answer is:

suspender

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'a brace?' is the definition.
(I know that brace can be written as suspender)

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

Can you help me to learn more?

(Other definitions for suspender that I've seen before include "One responsible for hold-up" , "Stocking-holding strap" , "Supporter" , "hangman?" , "Strap to hold up a stocking" .)

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

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