The most common and most likely answer to this crossword clue is the 7 letter word OLYMPIC
I've seen this crossword clue in The Times
O
L
Y
M
P
I
C
More clues leading to the result OLYMPIC
- Old Greek image that’s sacred, commonly including Mass
- Strange policy to introduce mile in these games
- Religious film omits an hour, but includes a minute, of certain events
- Kind of top athlete to change policy about entrant in Marathon
- Observers initially imply, wrongly, Charlie is like a legendary athlete
- It may precede record of compliancy formed after withdrawal of Congress
- Policy must change over month of games
- I comply with rearrangement of international events
- Devout Cockney member in charge of special games
- Greek airline policy Macedonia’s first problem
Buddy explains!

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