The most common and most likely answer to this crossword clue is the 10 letter word COMPLEXION
I've seen this crossword clue in The Guardian
C
O
M
P
L
E
X
I
O
N
Buddy explains!
The straight part
We know that "Character" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case character = complexion.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 COMPLEXION mean?
COMPLEXION noun- The combination of humours making up one's physiological "temperament", being either hot or cold, and moist or dry.
- The quality, colour, or appearance of the skin on the face.
- The outward appearance of something.
- Outlook, attitude, or point of view.
- (loanword, especially in scientific works translated from German) An arrangement.
- To give a colour to.