Might or won't be eaten by the vegetarian (4)

I believe the answer is:

beef

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'might' is the definition.
(thesaurus)

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

(Other definitions for beef that I've seen before include "Bovine flesh" , "Type of meat" , "it's unacceptable for vegetarian" , "Grouse - meat" , "Brawn; complaint" .)

I've seen this clue in the Evening Standard.

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