A teacher is an instructor, usually in a predefined subject or skill.
Bethany was a one-quarter Skagaran teacher who instructed primary school students. She instructed Humans during the day, and illegally instructed Skagarans at night. Bethany's teaching of her students involved having them use slats. In late 2153, after Enterprise NX-01 arrived at her planet, the Human inhabitants of the planet started to become more accepting of other cultures, and Bethany thereafter began to openly teach Skagarans, and Humans. (ENT: "North Star")
When Lieutenant James T. Kirk taught a class at Starfleet Academy, he was known for being a tough instructor. Gary Mitchell recalled being told by upperclassmen to watch out for him. (TOS: "Where No Man Has Gone Before")
In a classroom on Earth Two in 2266, a boy Only pretended to be a teacher, as a game, while surrounded by other Only children. However, one of them, Jahn, had to advise him on how a teacher would talk. When Jahn asked what a teacher would typically say, the other boy replied, "Study, study, study! Or bonk, bonk, bad kid." Although the boy at one point claimed he was a policeman, Jahn reminded him he was meant to be a teacher, to which the role-playing boy declared he had two jobs. Soon thereafter, Space Central arranged to send teachers and advisers to look after the children. (TOS: "Miri")
After arriving on space station Deep Space 9, Keiko O'Brien started a school and became the teacher there, schooling some station children, including some Bajorans, Nog, and Jake Sisko. (DS9: "A Man Alone") Later in 2369, her husband, Miles O'Brien, acted as a substitute teacher for the class. (DS9: "The Nagus")