Spectral clustering is a widely studied problem, yet its complexity is prohibitive for dynamic graphs of even modest size. We claim that it is possible to get information from past cluster assignments to expedite computation. Our approach builds on a recent idea of sidestepping the main bottleneck of spectral clustering, i.e., computing the graph eigenvectors, by using fast Chebyshev graph filtering of random signals. We show that the proposed algorithm achieves clustering assignments with quality approximating that of of spectral clustering and that it can yield significant complexity benefits when the graph dynamics are appropriately bounded.