The most common and most likely answer to this crossword clue is the 4 letter word GYRO
I've seen this crossword clue in Independent
G
Y
R
O
More clues leading to the result GYRO
Buddy explains!

The straight part
We know that "Greek dish" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case greek dish = gyro.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 GYRO mean?
GYRO noun- A gyroscope
- A gyrocompass
- An autogyro
- A style of Greek sandwich commonly filled with grilled meat, tomato, onions, and tzatziki sauce.