According to the Second Circuit:

This Court entered a temporary injunction in the above-captioned case on Friday, September 24, 2021 for administrative purposes pending decision by a three-judge panel. IT IS HEREBY ORDERED that the September 24 injunction is DISSOLVED. IT IS FURTHER ORDERED that the motion for an injunction pending appeal is DENIED.

That said, not getting vaccinated does not equal automatic termination. 

As the City explained in their opposition to the injunction, "even employees who object to vaccination... can elect to stay home and retain their positions while being placed on unpaid leave with healthcare until early September 2022... And even if plaintiffs decline the extended leave option, the earliest any steps would be taken to terminate their employment would occur in December 2021." 

So, "employees who fail to submit proof of having received one dose of vaccination by September 27, 2021, are to be placed on unpaid leave with health insurance the following day. [internal citation] But an employee who submits proof of vaccination before November 30, 2021, will be able to return to work within a week. [internal citation] And an employee who submits proof of vaccination thereafter, but before September 5, 2022, will be able to return to work within two weeks." 

As to accommodations, the City is granting accommodations "for a religious or medical" needs. However, an underlying arbitration on the matter set "an alternative to any statutory reasonable accommodation process... for the 2021-2022 school year" where the deadline for "any requests to be considered as part of this process... [was] no later than Monday, September 20, 2021, by 5:00 p.m." Therefore, any school employee who has not yet applied for an accommodation, CANNOT get one. 

The City's opposition summed this entire situation up nicely where it stated, "Put bluntly, plaintiffs do not have a substantive due process right to teach children without being vaccinated against a dangerous infectious disease."