Prime Minister's Office
Cabinet Office
noun
The prime minister's (総理) government is where he does all his governmenting. It's where the Japanese Prime Minister's Office (aka the Cabinet Office) is located as well.
総理府 was actually renamed 内閣府 in 2001, so you'd generally only use 総理府 to talk about the Cabinet Offices from back in the day.
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. It will help to know 総理 beforehand as well.
総理府の電話番号を知っていますか？
Do you know the phone number of the prime minister's office?
総理府次長がお前のことをさがしていたぞ。
The Deputy Director General of the Prime Minister's Office was looking for you.
彼女のことについては、総理府で働いているという以外には何も知らなかった。
I knew nothing about her except that she worked in the prime minister’s office.