Private
Privately-Run, Privately-Operated
noun, の adjective
I am the one who keeps this place standing. In other words, it's a private establishment — privately-run and privately-operated by ME!
私立 means "private" in the sense of a business, school, or other institution that's run by a private entity, rather than by the government or the state.
This is a jukugo word, which usually means on'yomi readings from the kanji. If you know the readings of your kanji you'll know how to read this as well.
Both 市立 (municipal) and 私立 (private) are pronounced as しりつ and it's hard to tell them apart when speaking. Although they're not official readings, people sometimes distinguish 市立 and 私立 by pronouncing them as いちりつ and わたくしりつ respectively.
私立の大学に入りたいです。
I want to join a private university.
日本のインターナショナルスクールは主に私立です。
International schools in Japan are mainly private.
もしかして私立ワニカニアカデミーの一年生ですか？
Are you perhaps a first grade student of the private school, WaniKani Academy?