Formation of stable, dense nanoparticle clusters is interesting due to both the underlying physics and use of nanoclusters in applications such as digital printing, imaging and biosensing, and energy storage. Here, we explore formation of nanoparticle clusters in dispersions of the model disk-shaped colloid Laponite. Under basic conditions, the model disk-shaped colloid Laponite forms a repulsive glass in water due to strong electrostatic interactions. Addition of a nonadsorbing polymer, the sodium salt of poly(acrylic acid) (PAA), induces a depletion attraction between particles. Through dynamic light scattering (DLS) and rheology, we see that the polymer initially causes a transition from the glassy phase to an ergodic fluid. Samples at higher particle concentration age to a weak nonergodic state, while samples at lower Laponite remain as fluids. As the strength of attraction between particles is increased, we find an increase in the fast relaxation time measured via dynamic light scattering (e.g., slowing of the short-time diffusion of a single particle). While this may in part be attributed to an increase in the ionic strength, the aging behavior and glass-fluid transition we observe appear to be unique to the presence of polymer, suggesting that depletion plays an important role. DLS data on the fluid samples were consistent with two widely spaced diffusive relaxation modes, corresponding to motion of single particles and motion of large clusters, although other slow dynamic processes may be present. On the basis of the estimated volume fraction and depletion attraction, we believe the Laponite-PAA suspensions to be either fluids of stable dusters or glasses of clusters, although it is possible that the nonergodic state we observe is instead a gel of clusters. Additionally, the cluster size was found to be stable for at least 120 days and was directly related to the polymer concentration. This may serve as an important means of tuning cluster size in products and processes based on dense nanoparticle assemblies.