Passes time in classical fashion (4)

I believe the answer is:

dies

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'passes' is the definition.

I don't understand the rest of the clue.

(Other definitions for dies that I've seen before include "twenty-four hours in Rome" , "Berkshire racecourse" , "Ceases to be, cutters" , "one day in ancient Rome" , "Departs" .)

I've seen this clue in The Guardian.

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