It is part of the verb "to grow in". The new tooth will 'fill in' the empty space in the mouth where the the old tooth has been knocked out. (in --> out 🙂) This expression is a bit like 'settle in'. If you move to a new school and you are given a place in one of the classes (where presumably there is an empty/ vacant space), your teacher might tell you that don't worry you will soon settle in. (You will soon be part of the class).

It’s basically a phrasal verb. You don’t need it in the sentence, but it makes the word “grow” a bit more specific. The tooth is not just growing, it’s growing INTO the gap that was left by the other tooth.

When referring to a tooth the phrase "grow in" refers to the tooth coming down out of the gum and moving into the empty space, so therefore, "grow in" "grow into the space"