Crossword Genius

No longer globally relevant when asleep (4,2,3,5)

Ross

I believe the answer is:

dead to the world

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'asleep' is the definition.
(thesaurus)

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

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(Other definitions for dead to the world that I've seen before include "Fast asleep" , "Sleeping" , "Sound asleep; unconscious" .)

I've seen this clue in The Daily Express.
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