The most common and most likely answer to this crossword clue is the 8 letter word BRAINBOX
I've seen this crossword clue in The Times
B
R
A
I
N
B
O
X
More clues leading to the result BRAINBOX
- Intellectual support given to receiver of emails
- Before batting supporter put suitable protection on cranium
- Clever person packaged undergarment?
- Intellectual is supporter in fight
- How an intellectual may spar with an opponent?
- Clever clogs support popular TV
- She’s jolly clever, having underwear packed!
- Underwear packed for one who’s smart
- Clever type getting support with folder for incoming messages
- Where emails arrive on underwear for intellectual?
Buddy explains!

The straight part
We know that "cranium" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case cranium = brainbox.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 BRAINBOX mean?
BRAINBOX noun- A very intelligent person.
- The head or skull (which encloses the brain).