noun
staffroom; teachers' lounge; faculty lounge
A room in a school where teachers work, prepare lessons, and relax. The term is straightforward and commonly understood.
放課後、教員室で先生に質問した。
After school, I asked the teacher a question in the staffroom.
Compound of 教員 (teacher) and 室 (room). The exact historical derivation is uncertain, but the meaning is transparent from its components.