Rich duke assuming king's role in castle (4)

I believe the answer is:

deep

I'm a little stuck... Click here to teach me more about this clue!

'rich' is the definition.
(I know that rich can be written as deep)

I can't explain the rest of the clue.

(Other definitions for deep that I've seen before include "late" , "greatly involved?" , "Mysterious" , "Cavernous" , "Intense -- extreme" .)

I've seen this clue in The Independent.

Want a hint initially instead of a full solution? Install my app