Criminal act of penniless priest (5)

I believe the answer is:

arson

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'criminal act' is the definition.
(arson is a crime)

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

(Other definitions for arson that I've seen before include "Incendiary crime" , "matchplay, say?" , "Malicious burning to destroy property" , "Sonar (anag.)" , "Incendiary act" .)

I've seen this clue in The Independent.

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