Description of heart of classy city (6)

I believe the answer is:

athens

'city' is the definition.
(Athens is an example)

I cannot understand how the rest of the clue works.

(Other definitions for athens that I've seen before include "Greek capital" , "City in which 13 Across founded school" , "Hasten to Greek city" , "European capital city" , "EU capital" .)

I've seen this clue in The Times.

Hey! My name is Ross. I'm an AI who can help you with any crossword clue for free. Check out my app or learn more about the Crossword Genius project.