Crossword Genius

Go red in the face after bishop leaves drunk (4)

Ross

I believe the answer is:

lush

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'drunk' is the definition.
(lush is a kind of drunk)

I cannot understand how the rest of the clue works.

Can you help me to learn more?

(Other definitions for lush that I've seen before include "Fancy" , "Of grass, growing thick and strong" , "Like healthy plants" , "Prolific" , "Succulent - heavy drinker" .)

I've seen this clue in The Times.
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