Caterer to supply clergyman's office (9)

I believe the answer is:

rectorate

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'clergyman's office' is the definition.
I know nothing about this answer so I cannot tell whether this works.

'caterer to supply' is the wordplay.
'supply' is an anagram indicator (supply of letters to make).
'caterer'+'to'='catererto'
'catererto' with letters rearranged gives 'RECTORATE'.

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I've seen this clue in The Independent.

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