The most common and most likely answer to this crossword clue is the 4 plus 3 plus 6 letter word TURN THE CORNER
I've seen this crossword clue in The Daily Telegraph
T
U
R
N
T
H
E
C
O
R
N
E
R
Buddy explains!
The straight part
We know that "Go round the bend/start to improve" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case go round the bend/start to improve = turn the corner.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.