The most common and most likely answer to this crossword clue is the 3 letter word ETH
I've seen this crossword clue in The Times
E
T
H
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 = eth.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 ETH mean?
ETH noun- A letter (capital Ð, small ð) introduced into Old English to represent its dental fricative, then not distinguished from the letter thorn, no longer used in English but still in modern use in Icelandic, the IPA and other phonetic alphabets to represent the voiced dental fricative "th" sound as in the English word then. The letter is also used in Faroese, but is generally silent in that language.