I knew nothing about her except that she worked in the prime minister’s office.
The prime minister's (総理) government is where he does all his governmenting. It's where the Prime Minister's office is located as well.
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.