Great admirer who got Dan to go dancing? (3)

I believe the answer is:

fan

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'great admirer' is the definition.
'fan' can be an answer for 'admirer' (fan is a kind of admirer). I am not sure about the 'great' bit.

I don't understand the remainder of the clue.

Can you help me to learn more?

(Other definitions for fan that I've seen before include "Cooling device for enthusiastic supporter" , "Great enthusiast" , "Cooling device for an ardent supporter" , "Cool - enthusiast" , "Aficionado" .)

I've seen this clue in the Evening Standard.

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