  Following our reformulation of sheaf-theoretic Virasoro constraints with
applications to curves and surfaces joint with Lim-Moreira, I describe in the
present work the quiver analog. After phrasing a universal approach to Virasoro
constraints for moduli of quiver-representations, I prove them for any finite
quiver with relations, with frozen vertices, but without cycles. I use partial
flag varieties which are special cases of moduli spaces of framed
representations as a guiding example throughout. These results are applied to
give an independent proof of Virasoro constraints for all Gieseker semistable
sheaves on $\mathbb{P}^2$ and $\mathbb{P}^1 \times \mathbb{P}^1$ by using
derived equivalences to quivers with relations. Combined with an existing
universality argument for Virasoro constraints on Hilbert schemes of points on
surfaces, this leads to the proof of this rank 1 case for any $S$ which is
independent of the previous results in Gromov-Witten theory.
