The most common and most likely answer to this crossword clue is the 6 plus 7 letter word HAIR’S BREADTH
I've seen this crossword clue in The Guardian
H
A
I
R
â
€
™
S
B
R
E
A
D
T
H
Buddy explains!
The straight part
We know that "Very small margin" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case very small margin = hair’s breadth.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.