The most common and most likely answer to this crossword clue is the 10 letter word PORTAMENTO
I've seen this crossword clue in The Daily Telegraph
P
O
R
T
A
M
E
N
T
O
More clues leading to the result PORTAMENTO
Buddy explains!

The straight part
We know that "glide — in cantor’s style" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case glide — in cantor’s style = portamento.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 PORTAMENTO mean?
PORTAMENTO noun- A smooth, gliding transition from one note to another; used especially with stringed instruments, and sometimes on brass.