The most common and most likely answer to this crossword clue is the 6 letter word COURSE
I've seen this crossword clue in Financial Times
C
O
U
R
S
E
More clues leading to the result COURSE
- What sounds like vulgar series of lectures maybe
- Way to use bad language, suppressing love
- Broadcast vulgar programme for students
- What sounds like rough plan of action
- Prescribed treatment unfinished we hear
- An opportunity to learn of this, naturally
- Stream for programme of study
- Old dons swear in classes
- Where horses race and hunt with dogs?
- Definitely short and sweet, perhaps
Buddy explains!

The straight part
We know that "classes" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case classes = course.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 COURSE mean?
COURSE noun- A sequence of events.
- A path that something or someone moves along.
- The lowest square sail in a fully rigged mast, often named according to the mast.
- (in the plural, courses) Menses.
- A row or file of objects.
- One or more strings on some musical instruments (such as the guitar, lute or vihuela): if multiple, then closely spaced, tuned in unison or octaves and intended to played together.
- To run or flow (especially of liquids and more particularly blood).
- To run through or over.
- To pursue by tracking or estimating the course taken by one's prey; to follow or chase after.
- To cause to chase after or pursue game.
- In due course; as a matter of course, as a natural result.
- Naturally, as would be expected; for obvious reasons, obviously.