The most common and most likely answer to this crossword clue is the 6 letter word CANTED
C
A
N
T
E
D
Buddy explains!

The straight part
We know that "On edge" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case on edge = canted.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 CANTED mean?
CANTED verb- To speak with the jargon of a class or subgroup.
- To speak in set phrases.
- To preach in a singsong fashion, especially in a false or empty manner.
- Of a blazon, to make a pun that references the bearer of a coat of arms.
- To sell by auction, or bid at an auction.
- To set (something) at an angle.
- To give a sudden turn or new direction to.
- To bevel an edge or corner.
- To overturn so that the contents are emptied.
- To divide or parcel out.
- Having angles.
- Inclined at an angle to something else; sloping.