The most common and most likely answer to this crossword clue is the 6 letter word IONIAN
I've seen this crossword clue in The Times
I
O
N
I
A
N
More clues leading to the result IONIAN
- Ancient Greek — one on island that has a name
- Ancient Greek edition I analysed in part
- Greek or Roman one found in island heading north
- One occupying island with name Odysseus, perhaps?
- Scottish John follows headless lion into sea
- Using some education I analyse ancient Greek
- Region of Asia Minor, north of some Greek islands
Buddy explains!

The straight part
We know that "Ancient Greek" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case ancient greek = ionian.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.