Edge closer up near wild horse (10)

I believe the answer is:

lippizaner

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'wild horse' is the definition.
Both the answer and definition are singular nouns.
Maybe you can see an association between them that I don't see?

'edge closer up near' is the wordplay.
'edge' becomes 'lip' (lip is a kind of edge).
'closer' becomes 'piz' (I can't justify this - if you can you should believe this answer much more).
'up' is an anagram indicator (letters get chucked up).
'near' anagrammed gives 'aner'.
'lip'+'piz'+'aner'='LIPPIZANER'

Can you help me to learn more?

(Another definition for lippizaner that I've seen is " Mount".)

I've seen this clue in The Guardian.

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