Women will start receiving letters for a CervicalCheck screening appointment from July 6 and the HSE expects to clear a backlog that built up because of Covid-19 by October.
The health authority is restarting the screening service with priority groups, including women needing to be recalled after one year and new cases.
HSE chief clinical officer, Dr Colm Henry, said the new HPV test would be used when screening started next month.
CervicalCheck, BreastCheck, Diabetic RetinaScreen and BowelScreen were suspended in March on public health advice due to the Covid-19 pandemic.
BreastCheck and BowelScreen will resume screening in September and Diabetic RetinaScreen will start screening again next month.
Dr Henry stressed the restarting of the screening programme was based on the assumption that there would be no worsening of the Covid-19 situation and restrictions continue to ease.
Diabetic retinopathy was relatively easy to restart but breast cancer screening was more complicated because people had to come a congregated setting in four static units in the country.
Dr Henry said BreastCheck's mobile units had “repurposed ” to allow for control measures so that when healthy people came for screening they felt safe and secure.
The health authority's chief executive, Paul Reid, said the average number of close contacts of Covid-19 positive cases was 4.6 and had increased “marginally” over the last few weeks.
He said the turnaround time from referral for a test to the time contact tracing has been completed was 1.78 days last week, which was well within their target.
Mr Reid also referred to figures from the World Health Organisation that showed Ireland was in the top six countries for testing.
However, surgery could take two to three times longer because of the planning and preparation involved.
A person undergoing surgery would need to be isolated for 14 days and must test negative for the coronavirus 72 hours before the planned procedure was due to take place.
Mr Reid said the HSE hoped to launch its contact tracing app next week but it would have to be brought to Cabinet first.
The health authority had been very clear about the data on the app that would be used to curb the spread of Covid-19.
“This (the app) is what we call a decentralised model so the data is held on the person's phone," he said.