The most common and most likely answer to this crossword clue is the 11 letter word REFORMATION
I've seen this crossword clue in The Daily Telegraph
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More clues leading to the result REFORMATION
Buddy explains!
The straight part
We know that "Improvement" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case improvement = reformation.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 REFORMATION mean?
REFORMATION noun- An improvement (or an intended improvement) in the existing form or condition of institutions or practices, etc.; intended to make a striking change for the better in social, political or religious affairs or in the conduct of persons or operation of organizations.
- Change or correction, by a court in equity, to a written instrument to conform to the original intention of the parties.