We explore glassy dynamics of dense assemblies of soft particles that are self-propelled by active forces. These forces have a fixed amplitude and a propulsion direction that varies on a timescale τp, the persistence timescale. Numerical simulations of such active glasses are computationally challenging when the dynamics is governed by large persistence times. We describe in detail a recently proposed scheme that allows one to study directly the dynamics in the large persistence time limit, on timescales around and well above the persistence time. We discuss the idea behind the proposed scheme, which we call “activity-driven dynamics”, as well as its numerical implementation. We establish that our prescription faithfully reproduces all dynamical quantities in the appropriate limit τp → ∞. We deploy the approach to explore in detail the statistics of Eshelby-like plastic events in the steady state dynamics of a dense and intermittent active glass.