Anybody who is eligible for a third dose of a vaccine will be contacted in due course, according to the HSE.
During the week, the National Immunisation Advisory Committee (NIAC) recommended that people with weaker immune systems should get a third dose of a Pfizer or Moderna jab.
Damien McCallion is the HSE's national lead for the vaccination programme.
He says the health service has started identifying those who need a further shot.
"Immunocompromised people with two doses will not get the same benefit as, say, someone who isn't immunocompromised.
"So this is a third dose to support their primary vaccination, rather than a booster as such.
"But in practical terms for us there are a very specific set of conditions and illnesses that have been recognised and identified by NIAC.
"And we're working those through now in terms of trying to see how we will identify those people, and offer them that third vaccine as part of their primary vaccination".
While the positivity rate among young people has dropped significantly in the past week.
The rate among people aged 15 to 24 has gone from 22% to 16% - and from 13% to 10% in those aged up to 14.
Referrals among 15 to 24-year-olds has also dropped sharply, however it is now highest among those aged zero to 14.
While 61% of 12 to 15-year-olds have so far signed up for a vaccine. Mr McCallion says this is a 'really good' figure.
"In terms of [the] percentage of people registered in that age bracket - 12 to 15 - nearly 61% are registered.
"And of those, the vast majority have already had their first dose of their vaccine.
"So we would encourage parents to read the information on HSE.ie - it sets out clearly the benefits and the risks - and encourage them to come forward and bring their children forward for vaccination.
"But we think that's a really good figure, 61%, at this stage it has been running for a couple of weeks for that younger age group."
It comes as walk-in vaccination clinics continue this weekend, with people who got a first dose of AstraZeneca now able to get a second dose of an mRNA vaccine.
It follows recently updated advice from NIAC on mixing and matching.
Anybody over the age of 12 can avail of a first or second dose of a Pfizer jab, without an appointment, at a selection of clinics this weekend.
People are advised to visit the HSE website for further details of times and locations.
Mr McCallion says the clinics can now do more.
"The one difference this weekend is we still offer dose one and dose two to everyone, but in addition - following recent NIAC advice - we're in a position to offer second doses of mRNA vaccines to a small number of people who previously had a vector vaccine i.e. AstraZeneca and who will now be able to avail of that this weekend."