The most common and most likely answer to this crossword clue is the 9 letter word CHARYBDIS
I've seen this crossword clue in The Times
C
H
A
R
Y
B
D
I
S
More clues leading to the result CHARYBDIS
- Big Eddy’s cautious, beady eyes
- Monster making one cautious — b*** hell!
- Wary bishop is hosting Democrat Eddy near Sicily
- Bubbling up by river in African country, is maelstrom
- Mythological character cautious about bids
- Hard to avoid a wrecking with Biscay, a legendary shipping hazard
- Sea monster, agitated by scar, hid
Buddy explains!
The straight part
We know that "Big Eddy" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case big eddy = charybdis.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.