When faced with high frequency streams of data, clustering raises theoretical and algorithmic pitfalls. We introduce a new and adaptive online clustering algorithm relying on a quasi-Bayesian approach, with a dynamic (i.e., time-dependent) estimation of the (unknown and changing) number of clusters. We prove that our approach is supported by minimax regret bounds. We also provide an RJMCMC-flavored implementation (called PACBO, see https://cran.r-project.org/web/packages/PACBO/index.html) for which we give a convergence guarantee. Finally, numerical experiments illustrate the potential of our procedure.