Crossword Genius

On air broadcast has split account of the priesthood (7)

Ross

I believe the answer is:

aaronic

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'on' is the definition.
Both the answer and definition are adjectives.
Perhaps you can see a link between them that I don't see?

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

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(Other definitions for aaronic that I've seen before include "Priestly" , "For clerical work" .)

I've seen this clue in The Sunday Times and The Times.
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