What’s cured sleeper (6)

I believe the answer is:

kipper

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'sleeper' is the definition.
(kip can mean sleep)

I don't understand the rest of the clue.

(Other definitions for kipper that I've seen before include "One drops off" , "Cured fish (one having forty winks?)" , "Preserved herring" , "Dried and smoked herring" , "One not awake" .)

I've seen this clue in The Times.

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