Tale is here in stale pudding (6)

I believe the answer is:

afters

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'pudding' is the definition.
(both can mean dessert)

I cannot understand how the rest of the clue works.

(Other definitions for afters that I've seen before include "Informal desserts may be faster" , "Tiramisu, possibly" , "Possibly fools" , "Pud" , "Informal desserts, puddings" .)

I've seen this clue in The Times.

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