The most common and most likely answer to this crossword clue is the 7 plus 8 letter word PRIVATE QUARTERS
I've seen this crossword clue in The Daily Telegraph
P
R
I
V
A
T
E
Q
U
A
R
T
E
R
S
Buddy explains!
The straight part
We know that "Own accommodation in the barracks?" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case own accommodation in the barracks? = private quarters.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.