Penniless clergyman causing offence (5)

I believe the answer is:

arson

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'offence' is the definition.
(crime of illegally starting a fire)

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

Can you help me to learn more?

(Other definitions for arson that I've seen before include "Incendiarism" , "Fire-raiser's crime" , "Pyromaniac crime" , "matchplay, say?" , "Crime of fire-setting (5)" .)

I've seen this clue in The Times.

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