The process of dynamical arrest, leading to formation of different arrested states such as glasses and gels, along with the closely related process of aging, is central for both basic research and technology. Here we report on a study of the time-dependent structural evolution of two aqueous Laponite clay suspensions at different weight concentrations. Neutron diffraction experiments have been performed with the near and intermediate range order diffractometer (NIMROD) that allows studies of the structure of liquids and disordered materials over a continuous length scale ranging from 1 to 300 Å, i.e., from the atomistic to the mesoscopic scales. NIMROD is presently a unique diffractometer, bridging the length scales traditionally investigated by small angle neutron scattering or small angle x-ray scattering with that accessible by traditional diffractometers for liquids. Interestingly, we have unveiled a signature of aging of both suspensions in the length scale region of NIMROD. This phenomenon, ascribed to sporadic contacts between Laponite platelets at long times, has been observed with the sample arrested as gel or as repulsive glass. Moreover, water molecules within the layers closest to Laponite platelets surface show orientational and translational order, which maps into the crystalline structure of Laponite.