The most common and most likely answer to this crossword clue is the 2 plus 5 plus 5 letter word WE THREE KINGS
W
E
T
H
R
E
E
K
I
N
G
S
Buddy explains!
The straight part
We know that "Carol" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case carol = we three kings.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.