Aqueous suspensions of Laponite with discotic particles are well-studied and find a wide range of applications in industry. A new direction of their implementation is polymer composites that can exhibit improved physical properties.We have studied the aging of aqueous suspensions of Laponite and sodium polystyrene sulfonate (PSS-Na) and both their microscopic (small-angle X-ray scattering, SAXS) and macroscopic (small amplitude oscillatory shear (SAOS) rheometry) properties. The concentration of Laponite, $C_L$, was fixed at 2.5% wt and concentration of PSS-Na, $C_p$, was varied within 0-0.5% wt (0-24.2~mM). It is shown that the adding of PSS-Na significantly accelerates the aging.Nevertheless, the systems were stable against the sedimentation, and the flocculation didnt occur. Polyelectrolyte induced the appearance of large-scale fractal heterogeneities, which became more compact in the course of the aging. Polyelectrolyte induced the appearance of large-scale fractal heterogeneities, which became more compact in the course of the aging.