It’s certainly true that most people start off by working as a TEFL teach overseas. But there are many other possibilities. You could work in a private language school or you might work in anything from a primary to a high school.
If you don’t fancy the idea of moving you could always teach online from the comfort of your own home.
Many TEFL teachers work by teaching in companies, in nurseries or kindergartens, or even in higher education colleges and universities. Although to do so you would probably need a few years’ experience first.
If you don’t fancy being a teacher, you could also become a language teacher’s teaching assistant in a public school (state school) or in some big chains of language schools.