The most common and most likely answer to this crossword clue is the 3 plus 3 letter word DOG EAR
I've seen this crossword clue in Financial Times
D
O
G
E
A
R
Buddy explains!
The straight part
We know that "Fold" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case fold = dog ear.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 DOG EAR mean?
DOG EAR noun- Folded corner of a page (as from a book or magazine, so as to mark one's place)
- To fold the corner of a book's page.