Many Jewish people grow up in American Ashkenazic homes without knowing that reincarnation is a Jewish concept. Reincarnation is not mentioned at all in the Talmud. The Talmud is the most fundamental part of Judaism. It is essential for its practice. Servitude is required to reincarnate, freedom is when the soul has reached enlightenment.
Further reincarnation is then no longer necessary.
The servant is free. Reincarnation like many other concepts of Jewish mysticism which are written in the Zohar are clarified and explained in depth by the Arizal in the writings of Chaim Vital his prize student. The Zohar relates the matter of Kabballah in a general way. The teachings of the Arizal are much more specific. All experts agree that without the teachings of the Arizal, it would be impossible to understand the Zohar.