Nikki Cohen, who owns Seacroft Pharmacy with her husband Ashley, praised the "fantastic turnout" on their first day of administering the jabs.
Over 50s, frontline health workers and those with underlying health conditions are being offered a third jab before winter sets in.
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Nikki said: "We've already had a lot of people who booked online but also a lot of people who have just turned out.
"Everybody is really motivated to get their Covid booster jab and protect themselves for the winter."
Nikki and Ashley last week appealed via the YEP for extra volunteers to help the vaccinations process.
Nikki added: "To be able to have this volume of people come through and have their vaccination we've had to employ new staff, train up vaccinators, we have a fantastic team of volunteers who come and marshals.
"We've got a lot of the over-80s in today and they need that little extra bit of support.
"Everyone just wants to have themselves as protected as possible.
"It's great that we've all had our first two vaccinations but we need to know that - as we go into the winter months especially, older people, people with underlying health conditions, all those over 50s that are going to be eligible - we can vaccinate as many people as possible."
Seacroft Pharmacy's vaccine clinics are held every Wednesday and Thursday from 8.30am-5.30pm at The Medical Centre, 846 York Road.