The most common and most likely answer to this crossword clue is the 3 plus 6 plus 2 plus 4 letter word TOO CLEVER BY HALF
I've seen this crossword clue in The Daily Telegraph
T
O
O
C
L
E
V
E
R
B
Y
H
A
L
F
Buddy explains!
The straight part
We know that "an arrogant know-all" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case an arrogant know-all = too clever by half.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.