All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
There is no harm in repairing a tooth that has been broken, as this is among seeking treatment. The Prophet said: "O slaves of Allaah, seek treatment." [At-Tirmithi and Abu Daawood]
As regards changing the front teeth other than the broken one or the one that had fallen, for the purpose of beautification or cheating so that the one who looks at them would think that they are original, then this is not permissible as this is considered changing the creation of Allaah which is forbidden according to the Book of Allaah and the Sunnah of the Prophet . Anyway, in conclusion, there is no harm in replacing fallen teeth, or removing any abnormality in them, or repairing broken ones, but removing a tooth without any necessity and just for the purpose of exchanging it with a better one, or reducing its width, or reshaping it and the like, then that is not permissible.
Allaah knows best.