Got up smartly (6)

I believe the answer is:

dressy

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'got' is the definition.
The answer and definition are not the same part of speech. However, past participle verbs and adjectives can occasionally define each other.

I cannot understand how the remainder of the clue works.

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(Other definitions for dressy that I've seen before include "Smartly clad, wearing stylish clothes" , "Stylishly attired" , "Smartly clothed" , "'Stylish, smart (6)'" , "swish" .)

I've seen this clue in The Globe and Mail and The Guardian.

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