One type of fan club (6)

I believe the answer is:

rotary

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'club' is the definition.
(Rotary Club is an example)

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

(Other definitions for rotary that I've seen before include "International club" , "Revolving round an axis" , "Sort of club" , "Revolving (like a club?)" , "Gyratory" .)

I've seen this clue in The Globe and Mail.

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