If they're working for and being paid by a public body, they're public sector.
Strangely enough I predicted that this would happen 18 Months ago - in particular in relation to the HSE but also in other sectors. Many of the thousands that retired are relatively young and healthy but also very experienced. You can't have a recruitment embargo at the same time that you're wiping away your top level of experienced staff, particularly when your workload is staying the same or increasing. That's a fact whether you're running the HSE or a Construction company.