The most common and most likely answer to this crossword clue is the 9 letter word LAMINATED
I've seen this crossword clue in The Daily Telegraph
L
A
M
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Buddy explains!

The straight part
We know that "separated into layers" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case separated into layers = laminated.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 LAMINATED mean?
LAMINATED verb- To assemble from thin sheets glued together.
- To cover something flat, usually paper, in adhesive protective plastic.
- To form, as metal, into a thin plate, as by rolling.
- To cause to separate into thin plates or layers; to divide into thin plates.
- Made by lamination.
- Consisting of many thin layers.
- (of rocks) Splitting into thin layers parallel to bedding.