Extremely important not to start appealing (4)

I believe the answer is:

cute

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'appealing' is the definition.
(I've seen this before)

I can't explain the rest of the clue.

(Other definitions for cute that I've seen before include "Winsome" , "Endearingly pretty" , "winning" , "Location" , "Endearing" .)

I've seen this clue in The Times.

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