That should be fine. The gender is rarely assumed, but in this context you would probably know the gender of the teacher, so there wouldn't really be a reason to use a gender neutral term. Often the sentence would be rewritten to exclude any references to gender, as there aren't really any gender neutral pronouns in Norwegian.
Sin is self-reflexive, so 'The teacher signs their own papers.' (I'm pretty sure the plural form 'sine' is used here because the object, 'papers', is plural.) We don't know the teacher's gender here. If 'hans' or 'hennes' are used in place of 'sine' it means an external person. 'The teacher is signing his/her (the student's) papers.'