The most common and most likely answer to this crossword clue is the 9 letter word STOP-OVER
I've seen this crossword clue in The Times
S
T
O
P
-
O
V
E
R
Buddy explains!
The straight part
We know that "brief stay" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case brief stay = stop-over.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 STOP-OVER mean?
STOP-OVER noun- A short interruption in a journey or the place visited during such an interruption.