The most common and most likely answer to this crossword clue is the 9 letter word CUBBYHOLE
I've seen this crossword clue in The Guardian
C
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B
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Buddy explains!

The straight part
We know that "small compartment" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case small compartment = cubbyhole.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 CUBBYHOLE mean?
CUBBYHOLE noun- A small, snug room which may be used as a place of privacy and safety by children
- A small compartment; a pigeonhole
- A glove compartment