Windy part of a kite? (4)

I believe the answer is:

reel

(Other definitions for reel that I've seen before include "Lively dance and angler's spool" , "blows making one do this?" , "Revolving spool" , "Dance; winding cylinder" , "Winding spool on a fishing rod" .)

I've seen this clue in The New York Times.

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