The most common and most likely answer to this crossword clue is the 6 letter word CRANIA
I've seen this crossword clue in The Guardian
C
R
A
N
I
A
More clues leading to the result CRANIA
- Brainboxes hurried to block agents
- Brainboxes managed to infiltrate US intelligence
- Brainboxes coming up with a popular line
- Managed to infiltrate intelligence agency’s protective structures
- Operated in group with lots of intelligence — they’re full of brains
- Brainboxes operated in intelligence group
- Brainboxes sought office in US protected by secret service
- Central Intelligence Agency has smuggled skulls
- Nutcases operated within intelligence service
Buddy explains!

The straight part
We know that "Brainboxes" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case brainboxes = crania.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 CRANIA mean?
CRANIA noun- The braincase or neurocranium; that part of the skull consisting of the bones enclosing the brain, but not including the bones of the face or jaw.
- The upper portion of the skull, including the neurocranium and facial bones, but not including the jawbone (mandible).
- The skull.