The most common and most likely answer to this crossword clue is the 8 letter word BARMIEST
I've seen this crossword clue in The Guardian
B
A
R
M
I
E
S
T
More clues leading to the result BARMIEST
Buddy explains!
The straight part
We know that "Most eccentric" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case most eccentric = barmiest.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 BARMIEST mean?
BARMIEST adjective- Odd, strange, or crazy.
- Containing barm, i.e. froth from fermented yeast.