DJ’s companion gave somebody a shiner, we’re told (5,3)

I believe the answer is:

black tie

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'dj's' is the definition.
Although both the answer and definition are singular nouns, I don't see how one could define the other.

I can't explain the rest of the clue.

Can you help me to learn more?

(Other definitions for black tie that I've seen before include "One accompanies DJ" , "Formal (neck)wear" , "Formal evening wear for men" , "Accompaniment of 11" , "expensive party-going habit" .)

I've seen this clue in The Times.

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