The most common and most likely answer to this crossword clue is the 6 letter word LYCEUM
I've seen this crossword clue in Independent
L
Y
C
E
U
M
More clues leading to the result LYCEUM
- My clue cooked up for Aristotle’s school
- College my clue represented
- Extremes of lethargy with taking English in? With which Eng. Lit. students are familiar
- Lecture-hall chimney lined by unknown engineer
- School story – see them in the auditorium?
- Where Lucy did the twist with me?
- My clue’s rubbish for classical school
- My clue involved a college
- One misses Miley C twerking, entertaining University College
- Me and Lucy travel for school
Buddy explains!

The straight part
We know that "classical school" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case classical school = lyceum.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.