Longman Dictionary of Contemporary English
upper school
noun
EXAMPLES FROM CORPUS
▪ Pupils will be taught in the upper school, across the valley, until governors get the council's full report.
▪ The upper school were remaining but it would be at least another week before he'd have to return.
Wikipedia
Upper school
Upper schools tend to be schools within secondary education. Outside England, the term normally refers to a section of a larger school. There is some variation in the use of the term in England.