Bayesian phylogenetic and phylodynamic analyses can be very time-consuming, owing to the combination of complex models that are used to estimate key parameters from increasingly large genomic data sets and their associated metadata. The use of high-performance computer hardware can -- to a certain extent -- alleviate the computational burden and markedly decrease the time to results. Still, even converging to the posterior can be a lengthy endeavour, with the burn-in aspect of such analyses potentially taking days or even weeks for large data sets. One of the key aspects that hampers performance in Bayesian phylogenetic inference is the efficiency with which tree topology proposals explore tree space. We here propose a novel adaptive tree transition kernel, which we call `subTreeLeap' (STL), which involves modifying the phylogeny by walking along patristic distance paths in the tree according to an adaptable radius parameter. STL is a general proposal, which can be used with contemporaneous or time-calibrated sequence data, being particularly suited to the latter due to respecting temporal precedence constraints. We carefully assess its impact on convergence and statistical mixing of the exploration of posterior tree space, by comparison to replicate ``golden runs'' obtained from lengthy analyses of empirical data under standard tree transition kernels. We find that STL successfully explores the same posterior tree space as standard kernels, but often does so in a more efficient manner. We discuss limitations as well as future potential improvements to STL that could substantially increase the speed at which Bayesian phylogenetic inferences are obtained.
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