Discredit duke and Archbishop taking heroin (8)

I believe the answer is:

disgrace

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'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 Sunday Times and The Times.

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