Within the Jewish schools of thought that affirm the idea of reincarnation (i.e. that a soul can return to Earth in order to correct mistakes),
Are there any new souls on Earth today?
How do we know if we have been reincarnated?
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אֵין בֶּן דָּוִד בָּא עַד שֶׁיִּכְלוּ כׇּל נְשָׁמוֹת שֶׁבַּגּוּף
The Messiah will not come till all the souls in the "body" are finished / completed.
Rashi there explains (מנשמות שבאותו אוצר ששמו גוף) that there is a store of souls whose name is "body", and that the Messiah will not come till all those souls have come to this world.
It follows that if the Messiah has not yet come that there are still new souls coming to this world.
Almost all souls that are born today came in multiple gilgulim already. New neshamos are extremely rare in these last generations, only great yechidei segulah merit new souls as they are very lofty. The Baal HaTanya in Likkutei Torah brings that there are two kinds, chadashos & chadashos mamash. Dovid HaMelech for example was a neshama chadasha but not mamash because although it was his first time in a physical guf he had already been in this world within the neshama of Adam HaRishon and therefore was not a neshama chadasha mamash. The latter on the other hand, are souls that weren’t even included within the neshama of Adam HaRishon which was comprised of all the Jewish souls except for those that will be born after techyias hameisim and some exceptions who are born before. The Baal Shemtov said about the Baal HaTanya that he was a neshama chadasha mamash entrusted with a special mission (neshamos chadashos don’t come for a tikkun prati) to reveal a new derech in Avodas Hashem and be a light in both nigleh and nistar, hence his name Shneur (shnei-or) the Baal HaTanya & Shulchan Aruch the two lights.