The most common and most likely answer to this crossword clue is the 8 letter word DIDACTIC
I've seen this crossword clue in Financial Times
D
I
D
A
C
T
I
C
More clues leading to the result DIDACTIC
- Used to pose insincerely, in charge of teaching
- Performed first part of play cold? That's edifying
- Played a part in charge of teaching
- Performed, I see, in manner of a teacher
- Visited polar region, getting shot of river that’s improving
- Performed deed in college, initially providing instruction
- As teacher performed start of play, with minimum of creativity
- Lift for police detaining ungentlemanly sort after appeal that’s instructive
- Addict, wrongly put in charge, is instructive
- Finished first scene with leading character as a teacher
Buddy explains!

The straight part
We know that "improving" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case improving = didactic.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 DIDACTIC mean?
DIDACTIC noun- A treatise on teaching or education.
- Instructive or intended to teach or demonstrate, especially with regard to morality.
- Excessively moralizing.
- Teaching from textbooks rather than laboratory demonstration and clinical application.