Apparatus to cool an ardent supporter (3)

I believe the answer is:

fan

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'supporter' is the definition.
(I know that supporter can be written as fan)

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

Can you help me to learn more?

(Other definitions for fan that I've seen before include "Spanish women wave it to cool themselves" , "Cooling device or disciple of performer" , "Devoted admirer or air cooler" , "Cooling device for an ardent supporter" , "Ardent admirer" .)

I've seen this clue in The Irish Independent.

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