This paper presents a new model for characterizing temporal dependence in exceedances above a given threshold. Our model is based on a class of stationary, infinitely divisible stochastic processes known as trawl processes. For use with extreme values, our model is constructed by embedding a trawl process in a hierarchical framework. This ensures that the marginal distribution is a generalized Pareto, as expected from classical extreme value theory. We also consider a modified version of this model that works with a wider class of generalized Pareto distributions (GPDs) and has the advantage of separating marginal and temporal dependence properties. The model is illustrated via various applications to environmental time series; thus, we show that the model offers considerable flexibility in capturing the dependence structure of extreme value data.