The most common and most likely answer to this crossword clue is the 9 letter word LAID-BACK
I've seen this crossword clue in The Guardian
L
A
I
D
-
B
A
C
K
More clues leading to the result LAID-BACK
Buddy explains!
The straight part
We know that "Cool" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case cool = laid-back.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 LAID-BACK mean?
LAID-BACK adjective- Relaxed and easy-going; an absence of stress or worry