In cavity quantum electrodynamics (cQED) and particularly superradiance, emitters are typically assumed to be independent, interacting only through light shared via a common mode. While such photon-mediated interactions lead to a rich spectrum of collective optical effects, direct dipole-dipole interactions within the emitter ensemble are generally viewed as a source of decoherence. Here, we uncover a new role for direct spin-spin interactions as a drive for the superradiant dynamics of a hybrid system of nitrogen-vacancy center spins in diamond coupled to a superconducting microwave cavity. After an initial fast superradiant burst, we observe an unexpected train of subsequent emission pulses followed by quasi-continuous masing for up to one millisecond. We show that this surprising behavior arises from spectral hole refilling, where spin inversion is redistributed into the superradiant window of spins resonant with the cavity. We report measurements that clearly exclude other cQED-related effects, and performed microscopic simulations of up to one million spins, which demonstrate that the observed self-induced masing is indeed driven by dipole-dipole interactions between the spins. These findings open new pathways for exploring complex spin-spin interactions in dense disordered systems and offer possibilities for ultra-narrow linewidth solid-state superradiant masers powered purely by microwave-driven spin control.