Duke with private theory about time they arrive to eat ... (6,6)

I believe the answer is:

dinner guests

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'time they arrive to eat' is the definition.
I know nothing about this answer so I cannot judge whether this works.

'duke with private theory' is the wordplay.
'duke' becomes 'd' (abbreviation).
'with' says to put letters next to each other.
'private' becomes 'inner' (as in one's private or inner thoughts).
'theory' becomes 'guests' (I can't explain this - if you can you should believe this answer much more).
'd'+'inner'+'guests'='DINNER GUESTS'

'about' acts as a link.

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I've seen this clue in The Guardian.

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