The most common and most likely answer to this crossword clue is the 7 plus 6 letter word PRIVATE SCHOOL
I've seen this crossword clue in The Guardian
P
R
I
V
A
T
E
S
C
H
O
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L
More clues leading to the result PRIVATE SCHOOL
- Where we learn the state does not pay?
- Top rival chose to work in Westminster perhaps
- Where one may be taught a lesson with ice down jockstrap, might you say?
- Hospital cover up that may provide a costly lesson
- Soldiers calm when guarding hospital or academic institution
- Soldiers relaxed around hotel in Harrow, say
Buddy explains!
The straight part
We know that "Where one may be taught a lesson" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case where one may be taught a lesson = private school.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.