Principal has no problem with cleric in gaol (6,8)

I believe the answer is:

prison chaplain

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'cleric in gaol' is the definition.
The definition and answer can be both people as well as being singular nouns.
Perhaps they are linked in a way I don't understand?

'principal has no problem' is the wordplay.
'problem' indicates anagramming the letters.
'principal'+'has'+'no'='principalhasno'
'principalhasno' is an anagram of 'PRISON CHAPLAIN'.

'with' is the link.

Can you help me to learn more?

(Another definition for prison chaplain that I've seen is " Can preacher".)

I've seen this clue in the Sydney Morning Herald.

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