According to the Rambam in Hilchos Mamarim 1 and 2, a Sanhedrin has enormous power. Roughly speaking, it oversees a) oral traditions, b) rabbinical enactments, and c) drashos: derivations using the י"ג מדות. At least for the drashos, the Rambam holds that the Sanhedrin can override any previous Sanhedrin, even if it was greater.
Assuming that this list contains pretty much everything we call "oral Torah", that should mean that the Sanhedrin can settle any question that isn't governed by a הלכה למשה מסיני, or some kind of תקנה דרבנן.
Any תיקו (the tradition is to read this homiletically, that Eliyahu will come and settle unanswered questions in the gemara). Certainly any later question in the Rishonim or Achronim.
Most decisions in the Shulchan Aruch and later are decided by ruling strictly among the Rishonim! The new Sanhedrin could instead just, pick one.
Or pick minhagim, between Ashkenazim and Sefardim and Yemenites. From now on, this is how we all do it.
That's without their power to actually make completely new drashos and simply override what the gemara or tannaim said.
What do we expect them to actually do? They could turn everything upside down! Do we expect them to do that, relitigate every question and essentially make every sefer we have obsolete? Or would they nibble at the edges, leaving most everything alone, respecting tradition, even though literally almost all of it is based on the earlier authorities not having the power to do what the Sanhedrin can do?
Would that be an abdication of the job that the Torah gave them explicitly (Devarim 17:8-11): to settle questions in a decisive way?
Is the approach taken by the Amoraim in the Talmudim relevant? The Rambam seemed to treat them as a quasi-Sanhedrin, able to make decisions that were binding on all of Israel - unlike any Beis Din that came after. Nevertheless, the Amoraim considered themselves bound by the ruling of the Tannaim. Is that because they weren't quite a Sanhedrin, or because that is the right approach?
Have gedolim offered opinions on how this would work?
Maybe a follow-up question (לולא מסתפני), if we think that they would turn everyone upside down: We might naively have assumed that qualification for the Sanhedrin is similar (with maybe a few additional requirements) to qualification for being a gadol today: great mastery of the Torah literature from the Gemara and onward. So the Sanhedrin would presumably be chosen from our gedolim.
But in the new Sanhedrin, is it possible that that skill set would no longer be very useful, since all those sefarim are about to become obsolete? Or would we say that the דעת תורה that this study granted those gedolim, is exactly the characteristic that the New Sanhedrin is going to need as well?
Update: The Kesef Mishnah on the Rambam I brought at the beginning says that even though they do have this power to relitigate drashos, the chachmei hagemara decided never to do it ("קימו וקיבלו") for the Mishnah, and later generations decided never to do it for the Talmud. When do they do that, and would it apply to a new Sanhedrin? Does that decision have the status of a "takanah", which has higher standards for being overriden (גדול בחכמה ובמנין, see there)? The Rambam seems to say elsewhere that no one after the Talmud was accepted like a Sanhedrin, so a real new Sanhedrin might be different.
I would expect that many areas of what in the west is known as civil and criminal law would be updated and brought into the 21st century. The scholarship of the Mishpat Ivri movement has already furnished a headstart in these areas, but there is obviously plenty more to do. I would expect that just about everything ritually related would remain mostly the same - other than whatever steps would need to be taken in order to harmonize the practices of various edoth.
– Deuteronomy Feb 03 '22 at 15:52