Otherwise working on said holy agency of public speaking (10)

I believe the answer is:

oratorical

'of public speaking' is the definition.

'otherwise working on said holy agency' is the wordplay.
'otherwise' becomes 'or'.
'working on' becomes 'at' (I've seen this in other clues).
'said' shows a homophone (sound like).
'holy agency' becomes 'oracle'.
'oracle' is a homophone of 'orical'.
'or'+'at'+'orical'='ORATORICAL'

(Another definition for oratorical that I've seen is " Relating to public speaking".)

I've seen this clue in The Telegraph.

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