The most common and most likely answer to this crossword clue is the 8 letter word CLAUSTRA
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Buddy explains!
The straight part
We know that "Brain layers" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case brain layers = claustra.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 CLAUSTRA mean?
CLAUSTRA noun- A thin, irregular sheet of grey matter underneath the inner part of the neocortex on both sides of the brains of mammals; its exact function is not understood, but it is believed to facilitate coordination between senses.