According to Kikar, Rav Yehuda Silman, a prominent posek in Bnei Braq, has paskened that teachers  - both in boys and in girls schools, in yeshivas and in seminaries - can be forced to vaccinate.

Additionally, Rav Silman paskens that an employer can obligate his employees to vaccinate. A Rosh Yeshiva can force the talmidim in the yeshiva to vaccinate or not let them come back to learn.

On the other hand Rav Silman also paskened regarding an avreich who missed time in kollel because he caught COVID-19 after refusing to vaccinate. The question asked was if the kollel could deduct that time from the stipend of the avreich, as the missed time was his own fault as he could have vaccinated. Rav Silman paskened that it should not be deducted form his stipend but he should be given the full stipend, until after Pesach.

I don't know what changes happen after Pesach. Maybe he feels that right now it is ok to insist on not vaccinating but after Pesach enough time will have passed that everyone should be vaccinated by then and one who is not yet vaccinated by Pesach is truly negligent and at fault.