The most common and most likely answer to this crossword clue is the 4 plus 4 plus 5 plus 2 letter word KEEP YOUR SHIRT ON
I've seen this crossword clue in The Daily Telegraph
K
E
E
P
Y
O
U
R
S
H
I
R
T
O
N
More clues leading to the result KEEP YOUR SHIRT ON
Buddy explains!
The straight part
We know that "Stay calm" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case stay calm = keep your shirt on.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.