Appointments have now started to be delivered to everyone in the 30 to 39-year-old age group after the focus fell on those in their 40s last week.
And it was also revealed that a key target is on course to be met.
Dr Mark Russell Lead for the Covid-19 vaccination programme in Lanarkshire, said: “We are on track to offer a first dose of the vaccination to all adults in Lanarkshire by the end of July.
"It’s now the turn of the 30 to 39 year-olds and we would encourage everyone who is offered an appointment to attend.
“However, we know that people have busy lives and the appointment offered may not be suitable.
"It’s very easy to reschedule your appointment to a more convenient time or place.
"You can do this online or by telephone – details are on your appointment letter.
"Also, make sure you cancel your appointment if you need to.
"This means that your appointment is then available for someone else to use and it is not wasted.”
Everyone in this age group will be offered the Pfizer vaccine, in line with national guidance from the Joint Committee on Vaccination and Immunisation .
Dr Russell added: “With different variants of Covid-19 emerging, attending your vaccination appointment is more important than ever. Covid-19 is still here and will be for some time.
"If we want to get back to doing the things we’ve missed, then we need to stick to the guidelines and get vaccinated.
"This will make sure we are doing all we can to protect ourselves and each other.
"It is also important to attend for your second dose as not doing so leaves the job half done and you are more vulnerable to becoming unwell due to the new variants we’re starting to see.”
More information on the local vaccination programme is available at www.nhslanarkshire.scot.nhs.uk/covid-19-vaccine. This includes dates for Muirfield Centre.