What could be held up by hatter, I bet (7)

I believe the answer is:

biretta

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'what could' is the definition.
I can't tell whether this definition defines the answer.

'held up by hatter i bet' is the wordplay.
'up by' says the letters should be written in reverse.
'held' says the answer is hidden in the clue.
'atterib' can be found hidden inside 'hatter i bet'.
'atterib' backwards is 'BIRETTA'.

'be' is the link.

Can you help me to learn more?

(Other definitions for biretta that I've seen before include "Stiff cap worn by Roman Catholic clergy" , "that covers a Catholic priest" , "Clergyman's cap" , "Battier (anag.)" , "ecclesiastical headgear" .)

I've seen this clue in The Times.

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