The most common and most likely answer to this crossword clue is the 4 plus 3 letter word PORK PIE
I've seen this crossword clue in The Guardian
P
O
R
K
P
I
E
More clues leading to the result PORK PIE
- The type of hat that can be eaten!
- . Kipper cooked with egg stuffing is Melton Mowbray’s claim to fame
- People making peanuts heading for insolvency in opening story
- In 26 without, say, a type of hat
- Popeye Doyle feature? One investigating chips in poker game
- Confusion follows humourless queen’s meeting with king
- Old recipe kitchen police included in mess food
- Type of hat that may be eaten
- Food with a fair amount of fat? That isn’t true
- Meat product, something hard to swallow?
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 = pork pie.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.