Private (establishment) — indicating an institution (e.g., school) run privately rather than by the government. Often contrasted with public (市立).
父は私立大学に通っていた。
My father attended a private university.
私立高校の入試は毎年競争が激しい。
Entrance exams for private high schools are highly competitive every year.
『しりつ』と読むが、紛らわしいときは『わたくしりつ』と言うこともある。
Although it's read 'shiritsu', when it's confusing people sometimes say 'watakushi-ritsu' to avoid ambiguity.