Riding improves broken chaos (2,9)

I believe the answer is:

on horseback

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'riding' is the definition.
I don't know anything about this answer so I can't judge whether this works.

'improves broken chaos' is the wordplay.
'improves' indicates an anagram (I've seen 'improve' mean this).
'broken'+'chaos'='brokenchaos'
'brokenchaos' anagrammed gives 'ON HORSEBACK'.

Can you help me to learn more?

(Other definitions for on horseback that I've seen before include "In the saddle" , "for such devils?" .)

I've seen this clue in The Daily Express.

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