The aging of water suspension of the synthetic clay Laponite has been studied by liquid-state triple-quantum filter nuclear magnetic resonance techniques, in a range of clay weight concentration (C-w = 0.012-0.028) known as the isotropic phase. Counterions dynamic parameters (rotational correlation time tau(c) and quadrupolar coupling constant e(2)qQ/h) have been extracted from sodium triple-quantum filtered experimental data within the multi-exponential quadrupolar relaxation theory in the fast exchange approximation. By monitoring quadrupolar sodium ions dynamical (tau(c) and e(2)qQ/h) and static (counterion concentration p(b)) properties during the aging, we find two different mechanisms of transition toward an arrested state. Our experimental findings match with the description which states, at low concentration, the formation of clusters of Laponite disks trigger the reaching of the arrested state, while at high concentration, single disks are the basic units of the arrested phase. The procedure proposed in this paper, based on multiple quantum filtered NMR data analysis, results to be a useful means to study the routes to arrested states in aqueous colloidal dispersions.