The aging dynamics after shear rejuvenation in a glassy clay suspension have been investigated through dynamic light scattering (DLS). Two different aging regimes are observed: one is attained if the sample is rejuvenated before its gelation and one after the rejuvenation of the gelled sample. In the first regime, the application of shear fully rejuvenates the sample, as the system dynamics soon after shear cessation follow the same aging evolution characteristic of standard aging. In the second regime, aging proceeds very fast after shear rejuvenation, and classical DLS cannot be used. An original protocol to measure an ensemble-averaged intensity-correlation function is proposed and its consistency with classical DLS is verified. The fast aging dynamics of rejuvenated gelled samples exhibit a power-law dependence of the slow relaxation time on the waiting time.