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Cook digesting broadcast about religious community (6)

Ross

I believe the answer is:

friary

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'religious community' is the definition.
Although both the answer and definition are singular nouns, I can't understand how one could define the other.

'cook digesting broadcast about' is the wordplay.
'cook' becomes 'fry' (frying is a type of cooking).
'digesting' is an insertion indicator (inserted letters are eaten or ingested).
'broadcast' becomes 'air' (to air on TV).
'about' shows that the letters should be reversed in order.
'air' written backwards gives 'ria'.
'fry' placed around 'ria' is 'FRIARY'.

Can you help me to learn more?

(Other definitions for friary that I've seen before include "Monastery" , "One's home to order" , "Place of the mendicant orders" , "House of Dominicans, for example" , "Religious establishment" .)

I've seen this clue in The Times.
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