The most common and most likely answer to this crossword clue is the 9 letter word SYSTEMISE
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More clues leading to the result SYSTEMISE
Buddy explains!

The straight part
We know that "Tidy up" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case tidy up = systemise.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does SYSTEMISE mean?
SYSTEMISE verb- To arrange into a systematic order.
- To engage in a cognitive process described as the drive to analyze and construct systems.