Muse wasting time with old age (3)

I believe the answer is:

era

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'age' is the definition.
(both can mean a long time)

I don't understand the remainder of the clue.

(Other definitions for era that I've seen before include "A particular period of time" , "Specific time" , "Long historical period" , "generation, maybe" , "Significant time" .)

I've seen this clue in The Guardian.

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