The most common and most likely answer to this crossword clue is the 8 letter word VOCALESE
V
O
C
A
L
E
S
E
Buddy explains!
The straight part
We know that "Jazz singer’s improvisation" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case jazz singer’s improvisation = vocalese.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 VOCALESE mean?
VOCALESE noun- Jazz singing genre where the lyrics are written to melodies that were originally parts of an all-instrumental composition or improvisation.