The most common and most likely answer to this crossword clue is the 6 letter word MADCAP
I've seen this crossword clue in The Sunday Telegraph
M
A
D
C
A
P
More clues leading to the result MADCAP
- Eccentric map includes a federal area for Washington
- Silly old lady and current old man coming back
- Crazy plan gone into by military assistant
- Reckless senior officer’s assistant enthralled by chart
- Crazy general's assistant enthralled by chart
- Eccentric adult duck occasionally interrupting plan
- Female returning contraceptive gets rash
- Reckless royal officer briefly disrupting plan
- Eccentric American duck oddly included in plan
- Crackpot erected wall, subject to financial limit
Buddy explains!

The straight part
We know that "Zany character" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case zany character = madcap.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 MADCAP mean?
MADCAP noun- An impulsive, hasty, capricious person.
- An insane person, a lunatic.
- Impulsive, hasty or reckless; capricious.