A hound will follow it all the way up (6)

I believe the answer is:

ascent

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'way up' is the definition.
(I've seen this before)

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

(Other definitions for ascent that I've seen before include "A climb or way up" , "(A) climb (up mountain)" , "Maybe promotion" , "rising?" , "advancement" .)

I've seen this clue in the Evening Standard.

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