A rapid pace of climate change is now becoming evident by a marked increase in the frequency and intensity of weather extremes, and this trend is expected to continue with an increase in global warming in the coming decades. The paper presents the linear extension of the Yule process (LEYP) as a general stochastic model of environmental hazards induced by non-stationary climate conditions. The LEYP is a more versatile model than the Poisson process, as it can incorporate dependence among events occurring over time. In the paper, explicit expressions have been derived for the return period, a traditional measure of reliability that is commonly used in the design of infrastructure systems. Unlike the stationary climate, the return period between extreme events would continue to decrease as climate change effects would become more pronounced in the future. Examples presented in the paper demonstrate that a modest degree of statistical dependence among events leads to a significant reduction in the return period, i.e., a remarkable increase in the frequency of extreme events. Therefore, existing design codes would need to be revised to accommodate such non-stationary changes to ensure a high level of safety of infrastructure systems in the changing climate.