The most common and most likely answer to this crossword clue is the 6 letter word SCREWY
I've seen this crossword clue in The Times
S
C
R
E
W
Y
Buddy explains!

The straight part
We know that "Eccentric" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case eccentric = screwy.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 SCREWY mean?
SCREWY adjective- Crazy; silly; ridiculous
- Tipsy; slightly drunk.
- Exacting; extortionate; close.
- Worthless.