The most common and most likely answer to this crossword clue is the 6 letter word SPARTA
I've seen this crossword clue in The Sunday Telegraph
S
P
A
R
T
A
More clues leading to the result SPARTA
- Austere city’s role in South Africa…
- It has drawn some in place of austerity
- Military city to practise fighting with part-time soldiers
- Greek city corners recalled Athens at first
- Old city region entertained by religious group
- Ambushes set up next to a city long ago
- Where Paris took Helen painting in spring
- Ancient city strikes back with part-time soldiers
- Ancient city in Cyprus?
- Practise fighting soldiers: no comfort here
Buddy explains!

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