The most common and most likely answer to this crossword clue is the 7 plus 3 plus 7 plus 5 letter word THROUGH THE LOOKING GLASS
I've seen this crossword clue in The Times
T
H
R
O
U
G
H
T
H
E
L
O
O
K
I
N
G
G
L
A
S
S
Buddy explains!
The straight part
We know that "Story" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case story = through the looking glass.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.