Recent experiments and simulations have revealed glassy features in the cytoplasm, living tissues as well as dense assemblies of self propelled colloids. This leads to a fundamental question: how do these non-equilibrium (active) amorphous materials differ from conventional passive glasses, created either by lowering temperature or by increasing density? To address this we investigate the aging behaviour after a quench to an almost arrested state of a model active glass former, a Kob-Andersen glass in two dimensions. Each constituent particle is driven by a constant propulsion force whose direction diffuses over time. Using extensive molecular dynamics simulations we reveal rich aging behaviour of this dense active matter system: short persistence times of the active forcing lead to effective thermal aging; in the opposite limit we find a two-step aging process with active athermal aging at short times followed by activity-driven aging at late times. We develop a dedicated simulation method that gives access to this long-time scaling regime for highly persistent active forces.