class teacher; homeroom teacher; form teacher
Refers to the teacher in charge of a particular class or homeroom in a school setting. The phrase is a common noun expression.
I consulted my homeroom teacher about my career path.
The new class teacher is very kind.
担任 alone means 'homeroom teacher' or 'class teacher' and is often used in school contexts, but 担任の先生 is a more explicit and polite way to refer to the teacher.
Phrase composed of 担任 (class charge) + の (possessive particle) + 先生 (teacher). The word 担任 itself is a Sino-Japanese compound meaning 'being in charge of a class'.