The most common and most likely answer to this crossword clue is the 8 letter word PALESTRA
I've seen this crossword clue in The Guardian
P
A
L
E
S
T
R
A
More clues leading to the result PALESTRA
Buddy explains!

The straight part
We know that "where classical training took place" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case where classical training took place = palestra.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 PALESTRA mean?
PALESTRA noun- A public area in ancient Greece and Rome dedicated to the teaching and practice of wrestling and other sports; a wrestling school, a gymnasium.
- An arena for literal or figurative combat; a battlefield.