Highly smitten in a batty sort of way? (5)

I believe the answer is:

skied

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'highly smitten' is the definition.
Although both the answer and definition are past participle verbs, I don't see how they can define each other.

I don't understand the rest of the clue.

Can you help me to learn more?

(Other definitions for skied that I've seen before include "took part in winter sport" , "Sported" , "having knocked up" .)

I've seen this clue in the Evening Standard.

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