The most common and most likely answer to this crossword clue is the 4 plus 5 letter word COME ROUND
I've seen this crossword clue in The Times
C
O
M
E
R
O
U
N
D
Buddy explains!
The straight part
We know that "Don’t stay out/visit" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case don’t stay out/visit = come round.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.