They may be on the drink — or the drink may be on them! (8)

I believe the answer is:

coasters

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'they' is the definition.
Both the answer and definition are plural nouns.
Maybe they are linked in a way I don't understand?

I don't understand how the rest of the clue works.

Can you help me to learn more?

(Other definitions for coasters that I've seen before include "Merchant ships with a limited range of operation" , "Small table-mats" , "Small mats for Socrates" .)

I've seen this clue in The Guardian.

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