Hampshire's health experts say these people are the most at risk of severe hospitalisations - even with the less potent Omicron variant.
Surveys suggest that while some remain unconvinced by the science behind the vaccine, there are others who simply 'haven't got round' to being vaccinated.
Now, celebrity help could be enlisted to get those people jabbed.
At Hampshire County Council's health and adult social care select committee, Cllr Alan Dowden said: 'There are a number of people still reluctant to take this vaccine - a certain tennis player springs to mind and that hadn't helped things.
'Across Hampshire there are quite a lot of celebrities who could help us with the vaccine effort. It would be very helpful - but they would have to be asked.
'Footballers, popstars and TV personalities being at vaccine centres would definitely encourage more people to walk through the doors.'
Fratton Park in Portsmouth has previously held pop-up vaccination events.
Dr Derek Sandeman, chief medical officer for Hampshire and Isle of Wight Integrated Care System, said: 'When we've done surveys there are many reasons they haven't been vaccinated.
'There is a huge industry of misinformation that is thriving at the moment - we don't necessarily have the skills to combat that.
'But I do agree that some celebrity involvement may well get more people vaccinated, either for the first time or for booster jabs.'
The number of Covid-19 cases in Hampshire has increased over the past few weeks.
The rate of infection has risen from 742 per 100,000 people on December 15 to 903.6 on January 12.
However, it is believed that this trend is starting to shift.
Dr Joanna Jeffries, the county council's assistant director of public health, said: 'In terms of the general picture we have Covid cases increasing across Hampshire, but are starting to see this figure stabilise.
'If I were optimistic I would say it's starting to decrease.
'We have seen some more robust decreases in the 60+ population, so that is certainly good news.'