The most common and most likely answer to this crossword clue is the 4 letter word IRIS
I've seen this crossword clue in The Daily Telegraph
I
R
I
S
More clues leading to the result IRIS
- Flower one gentleman brought up
- One pruned spring flower
- Independent is carrying leader on Rupert Murdoch
- Back away from national flag
- Girl — one teacher knocked over
- I dare dropping king's flag
- Flower from the Emerald Isle? Not quite!
- Flag initially identified by retired teacher?
- Girl is touring Rhode Island
- Cut Hibernian flag
Buddy explains!

The straight part
We know that "Eye part" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case eye part = iris.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 IRIS mean?
IRIS noun- A plant of the genus Iris, common in the northern hemisphere, and generally having attractive blooms (See Iris (plant)).
- The contractile membrane perforated by the pupil, which adjusts to control the amount of light reaching the retina, and which forms the colored portion of the eye (See Iris (anatomy)).
- A diaphragm used to regulate the size of a hole, especially as a way of controlling the amount of light reaching a lens.
- A rainbow, or other colourful refraction of light.
- A constricted opening in the path inside a waveguide, used to form a resonator.
- The inner circle of an oscillated color spot.
- (of an aperture, lens or door) To open or close in the manner of an iris.