The most common and most likely answer to this crossword clue is the 4 letter word INCH
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More clues leading to the result INCH
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 = inch.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 INCH mean?
INCH noun- A unit of length equal to one twelfth of a foot, or exactly 2.54 centimetres.
- The amount of water which would cover a surface to the depth of an inch, used as a measurement of rainfall.
- The amount of an alcoholic beverage which would fill a glass or bottle to the depth of an inch.
- A very short distance.
- (followed by a preposition) To advance very slowly, or by a small amount (in a particular direction).
- To drive by inches, or small degrees.
- To deal out by inches; to give sparingly.
- A small island