Fairground attraction regularly exhibited reindeer (4)

I believe the answer is:

ride

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'fairground attraction' is the definition.
(I've seen this in another clue)

I don't understand the rest of the clue.

(Other definitions for ride that I've seen before include "Travel (on a bike, perhaps)" , "spin > lift > pedal" , "Journey on horseback" , "Travel by horse, bus, etc" , "Lie at anchor" .)

I've seen this clue in The Independent.

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