A clinic to vaccinate Martha’s Vineyard public school teachers will begin Thursday, hospital and high school leaders announced this week.

The clinic has already filled 250 vaccination slots for public school educators and is scheduled to take place Thursday from 4 p.m. to 8 p.m.

Teachers and educators become eligible for the vaccine on March 11, after an order from Gov. Charlie Baker last week. Residents 65 and older, and those with two or more underlying conditions, continue to be eligible as well, hospital officials said in a briefing Wednesday.

Head nurse and chief operations officer Claire Seguin said 250 public school teachers had already registered for appointments, filling all available slots for Thursday’s clinic. Registration opened Monday evening and was conducted separately from the hospital’s weekly appointment scheduling. Educators were also able to sign up for appointments individually through the hospital’s general registration, Ms. Seguin said.

At a regional high school committee meeting Monday, school superintendent Matthew D’Andrea said according to a survey put out to school staff in February, 560 of the estimated 600 total faculty members in the public school system had signaled their desire for a vaccine. Some had already received their shot as part of a different eligibility category, he also said.

Hospital CEO Denise Schepici said Wednsday that the hospital hopes to further expand appointments for teachers, as with all other registration, when more vaccine becomes available through the state and federal supply.

“We will treat this as first-come, first-serve, depending on the amount of dosages that we get so we’ll open up more of the schedules if we have more dosages,” Ms. Schepici said.

In the interim, plans for a second all-teacher clinic are in the works, pending approval from the state, Ms. Seguin said.

At the school meeting Monday, Mr. D’Andrea said he hopes the subsequent clinic will complete vaccinations for the majority of interested faculty and staff.

“Teachers are getting out there and getting vaccinated and with these two clinics, I’m fairly confident we’re going to be able to have everyone vaccinated,” he said.

As of Tuesday at 5 p.m., the hospital had vaccinated 4,827 Islanders, 2,310 of which have received a second dose. Ms. Seguin said the hospital expects to vaccinate 1,245 more people with their first doses this week.

The hospital will continue vaccine registration for all eligible Islanders twice weekly on Mondays at 5 p.m. and Saturdays at 8 a.m. Ms. Seguin said she is optimistic that the hospital will receive vaccines for next week, though supply continues to depend on the state and federal government.

“We are encouraged by our conversations earlier this week that we will get vaccine supply for next week,” Ms. Seguin said. “That’s how we’re taking it one week at a time.”

Also Wednesday, Ms. Schepici and Ms. Seguin announced that the hospital has been listed among the top 100 critical access hospitals in the United States in an annual ranking from the Chartis Center for Rural Health.

Both took a minute to reflect on the ranking as the Island reaches the first anniversary of the virus lockdown this week.

“This recognition speaks to the hard work and teamwork that all the women and men of our hospital dedicate themselves to each and every day and I could not be prouder,” Ms. Schepici said. “It’s been a tough year. This is a team that shows it cares.”