The most common and most likely answer to this crossword clue is the 3 plus 6 plus 4 letter word THE BERLIN WALL
I've seen this crossword clue in The Guardian
T
H
E
B
E
R
L
I
N
W
A
L
L
Buddy explains!
The straight part
We know that "element of long division" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case element of long division = the berlin wall.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.