Microbial population genetics models often assume that all lineages are constrained by the same effective population size function over time. However, many neutral and selective events can invalidate this assumption, and contribute to the clonal expansion of a specific lineage relative to the rest of the population. This is characterised by rapid growth of the lineage, starting from a single new variant. Clonal expansions can happen for example due to gain of antibiotic resistance, imports into a wholly susceptible population, or changes in interventions during an epidemic. Such differential phylodynamic properties between lineages result in asymmetries and imbalances in phylogenetic trees that are often described informally but difficult to analyse formally. To this end, we developed a model under the coalescent framework describing how clonal expansions occur in terms of effective population size and affect the branching patterns of a phylogeny. We show how the parameters of this model can be inferred from a given dated phylogeny using Bayesian methodology, which allows us to assess the probability that one or more clonal expansion events occurred. For each putative clonal expansion event we estimate their date of emergence and subsequent phylodynamic trajectories, including their long-term evolutionary potential which is important to determine how much effort should be placed on specific control measures. We demonstrate the usefulness of our methodology on simulated and real datasets.