Sweet kitty taking medicine rolled around (8)

I believe the answer is:

lollipop

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'sweet' is the definition.
(lollipop is a kind of sweet)

I can't explain the rest of the clue.

(Other definitions for lollipop that I've seen before include "Sweet on a stick" , "Candy on a stick" , "Confectionery" , "Sweetmeat" , "Sweet; popular work" .)

I've seen this clue in The Sunday Times and The Times.

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