The most common and most likely answer to this crossword clue is the 13 letter word STRAW-BREADTH
S
T
R
A
W
-
B
R
E
A
D
T
H
Buddy explains!

The straight part
We know that "a whisker" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case a whisker = straw-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.