The influence of an applied shear field on the dynamics of an aging colloidal suspension has been investigated by the dynamic light-scattering determination of the density autocorrelation function. Though a stationary state is never observed, the slow dynamics crosses between two different nonequilibrium regimes as soon as the structural relaxation time tau(s) approaches the inverse shear rate gamma (-1) . In the shear-dominated regime (at high gamma values) the structural relaxation time is found to be strongly sensitive to the shear rate ( tau(s) approximately gamma (-alpha) , with alpha approximately 1 ) while aging proceeds at a very slow rate. The effect of the shear on the detailed shape of the density autocorrelation function is quantitatively described, assuming that the structural relaxation process arises from the heterogeneous superposition of many relaxing units, each one independently coupled to shear with a parallel composition rule for time scales: 1/tau-->1/tau+A gamma .