The most common and most likely answer to this crossword clue is the 4 letter word COED
I've seen this crossword clue in The Times
C
O
E
D
Buddy explains!

The straight part
We know that "School" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case school = coed.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 COED mean?
COED noun- A young woman who attends college.
- A (generally young) woman, especially on the campus of a college or other educational institute.
- Of an educational institution, that teaches both males and females.
- Of any location, that mixes males and females.