A new numerical framework based on Stokesian dynamics is used to study a shear-induced glass-to-crystal transition in suspensions of clay-like anisotropically charged platelets. The structures obtained in quiescent conditions are in agreement with previous Monte Carlo results: a liquid phase at very short interaction range (high salt concentration), phase separation and a gel without large scale density fluctuations at intermediate interaction ranges, and glassy states at very large interaction ranges. When initially glassy suspensions are sheared, hydrodynamic torques first rotate platelets so they can reach a transient quasi-nematic disordered state. These orientational correlations permit to unlock translational degrees of freedom and the platelets then form strings aligned with the velocity direction and hexagonally packed in the gradient–vorticity plane. Under steady shear, platelet orientations are correlated but the system is not nematic. After flow cessation and relaxation in quiescent conditions, positional and orientational order are further improved as the platelet suspension experiences a transition to a nematic hexagonal crystal. Energy calculations and the existence of residual stress anisotropy after relaxation show that this final structure is not an equilibrium state but rather a new ordered, arrested state. The transient, nematic, disordered state induced by shear immediately after startup and unlocking translational degrees of freedom is thought to be an initial step that may be generic for other suspensions of strongly anisotropic colloids with important translation-orientation coupling induced by long-range interactions.