Come down from Clydesdale? (8)

I believe the answer is:

dismount

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'come down' is the definition.
(dismounting is a kind of coming down)

I cannot understand how the rest of the clue works.

Can you help me to learn more?

(Other definitions for dismount that I've seen before include "Get off a horse/bicycle" , "Cease to ride" , "Alight from a horse or bicycle" , "Desert Arab perhaps" , "Get down, from bike or horse" .)

I've seen this clue in The Sun and The Times.

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