Discredit duke and Archbishop taking heroin (8)

I believe the answer is:

disgrace

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

'discredit' is the definition.
(I know that discredit can be written as disgrace)

I cannot understand how the remainder of the clue works.

Can you help me to learn more?

(Other definitions for disgrace that I've seen before include "Loss of reputation as the result of dishonourable action" , "Loss of good reputation" , "scandalous" , "Dishonour, ignominy" , "scandal" .)

I've seen this clue in The Times and The Sunday Times.

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