Question: Is one allowed to sit in Shul during the hakafos on Simchas Torah, or do they need to stand as the Torah is moving around?
Answer: The Shulchan Aruch (YD 282:2) writes that one must stand when the Sefer Torah is being carried until it has reached its destination or is out of sight (See Mishna Berura 146:17).
On Simchas Torah, when the Sifrei Torah are being carried for lengthy hakafos, this can be problematic for some who struggle to stand for long periods of time. Many of the poskim have come up with different solutions.
The Aruch Hashulchan (YD 282:5) writes that while one must stand during the hakafos, that only applies so long as the Sifrei Torah are in motion. In between the hakafos one may sit, whether the Sifrei Torah are on the bima or being held by others, as this counts as them having reached their destination.
R’ Shlomo Zalman Auerbach (Halichos Shlomo, Tefilla 12:13; Sukkos 12:9) maintained that the whole shul could be considered as the place of the Sifrei Torah during the hakafos. Additionally, if one sits outside of the circle, the people dancing can be considered to create an effective mechitza. Therefore, one may even sit during the hakafos if necessary. Nonetheless, as the first hakafa is the most important, one should at least stand for the first one. R’ Betzalel Stern (Betzel Hachachma 5:139:6) adds that just as one does not to repeatedly stand for an old person every time they pass, so too one can sit after the first hakafa if necessary (See Teshuvos Vehanhagos 2:319).
In conclusion, one should try their utmost to stand for the first hakafa. One may sit in between hakafos, and, if necessary, during the following hakafos.