Busy preparing for wedding (7)

I believe the answer is:

engaged

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'busy' is the definition.
(I know that busy can be written as engaged)

I don't understand how the rest of the clue works.

Can you help me to learn more?

(Other definitions for engaged that I've seen before include "Plighted; hired" , "May as well ring off" , "looking forward to the match?" , "being committed to union" , "Promised in marriage" .)

I've seen this clue in The Times.

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