It's possible, but in fact with an aging population we probably anticipate the opposite—that is, fewer people being in the labour force, fewer people working. That would not be because there weren't enough jobs, but because there were not enough people of working age. People 65 and over may well want to work, or some of them may very well be capable of working, but as they get older and older, they are less inclined to work.
What is likely to happen, all other things being equal, is a decline in the unemployment rate over the medium and longer term as people get older and there are fewer people available to fill the jobs that do exist. All of that is based on long-term demographics. Of course, there could be economic shocks, like the one we are currently living, that turn this on its head, but the longer-term trend is of an aging population and a declining unemployment rate—all other things being equal, of course.