Most studies evaluating future changes in climate extremes over Australia have examined events that occur once or more each year. However, it is extremes that occur less frequently than this that generally have the largest impacts on sectors such as infrastructure, health and finance. Here we use an ensemble of high resolution (similar to 10 km) climate projections from the NSW and ACT Regional Climate Modelling (NARCliM) project to provide insight into how such rare events may change over southeast Australia in the future. We examine changes in the frequency of extremes of heat, rainfall, bushfire weather, meteorological drought and thunderstorm energy by the late 21st century, focusing on events that currently occur once every 20 years (those with a 5% Annual Exceedance Probability). Overall the ensemble suggests increases in the frequency of all five extremes. Heat extremes exhibit the largest change in frequency and the greatest ensemble agreement, with current 1-in-20 year events projected to occur every year in central Australia and at least every 5 years across most of southeast Australia, by the late 21st century. The five capital cities included in our model domain are projected to experience multiple climate extremes more than twice as frequently in the late 21st century, with some cities projected to experience 1-in-20 year events more than six times as frequently. Although individual simulations show decreases in some extremes in some locations, there is no strong ensemble agreement for a decrease in any of the climate extremes over any part of southeast Australia. These results can support adaptation planning and should motivate further research into how extremely rare events will change over Australia in the future.