Be faster than the others when there’s a sudden exodus (7)

I believe the answer is:

outrush

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'be' is the definition.
Both the answer and definition are singular nouns.
Perhaps you can see a link between them that I can't see?

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

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(Another definition for outrush that I've seen is " A sudden release".)

I've seen this clue in the Evening Standard.

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