The most common and most likely answer to this crossword clue is the 6 letter word PEEPER
I've seen this crossword clue in Financial Times
P
E
E
P
E
R
Buddy explains!

The straight part
We know that "eye" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case eye = peeper.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 PEEPER mean?
PEEPER noun- (chiefly in the plural) The eye.
- Someone who peeps; a spy.
- A private detective.
- A peeping tom.
- An animal, such as some frogs, having a shrill, high-pitched call.
- A chicken just breaking the shell; a young bird.