The most common and most likely answer to this crossword clue is the 10 letter word FANCY-FREE
I've seen this crossword clue in The Guardian
F
A
N
C
Y
-
F
R
E
E
Buddy explains!
The straight part
We know that "without a care in the world" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case without a care in the world = fancy-free.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 FANCY-FREE mean?
FANCY-FREE adjective- Free of commitments or obligations
- Having no spouse or other partner