The most common and most likely answer to this crossword clue is the 8 letter word BORDERED
I've seen this crossword clue in The Daily Telegraph
B
O
R
D
E
R
E
D
More clues leading to the result BORDERED
Buddy explains!

The straight part
We know that "Given an edge" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case given an edge = bordered.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 BORDERED mean?
BORDERED verb- To put a border on something.
- To form a border around; to bound.
- To lie on, or adjacent to, a border of.
- To touch at a border (with on, upon, or with).
- To approach; to come near to; to verge (with on or upon).