The most common and most likely answer to this crossword clue is the 9 letter word SECONDARY
I've seen this crossword clue in Independent
S
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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 = secondary.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 SECONDARY mean?
SECONDARY noun- Any flight feather attached to the ulna (forearm) of a bird.
- An act of issuing more stock by an already publicly traded corporation.
- The defensive backs.
- An inductive coil or loop that is magnetically powered by a primary in a transformer or similar
- One who occupies a subordinate or auxiliary place; a delegate deputy.
- A secondary circle.
- A satellite.
- A secondary school.
- Anything secondary or of lesser importance.
- Next in order to the first or primary; of second place in origin, rank, etc.
- Originating from a deputy or delegated person or body
- Derived from a parent compound by replacement of two atoms of hydrogen by organic radicals
- Produced by alteration or deposition subsequent to the formation of the original rock mass.
- Developed by pressure or other causes.
- Pertaining to the second joint of the wing of a bird.
- Dependent or consequent upon another disease, or occurring in the second stage of a disease.
- Of less than primary importance.
- Related to secondary education, i.e. schooling between the ages of (approximately) 11 and 18.
- Relating to the manufacture of goods from raw materials.
- (of a color) Formed by mixing primary colors.
- Representing a reversion to an ancestral state.