The most common and most likely answer to this crossword clue is the 5 letter word BEVEL
I've seen this crossword clue in Financial Times
B
E
V
E
L
More clues leading to the result BEVEL
Buddy explains!

The straight part
We know that "edge" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case edge = bevel.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 BEVEL mean?
BEVEL noun- An edge that is canted, one that is not a 90-degree angle; a chamfer.
- An instrument consisting of two rules or arms, jointed together at one end, and opening to any angle, for adjusting the surfaces of work to the same or a given inclination; a bevel square.
- To give a canted edge to a surface; to chamfer.
- Having the slant of a bevel; slanting.
- Morally distorted; not upright.