Simulations are carried out for linear shear flow past a rotating elliptic cylinder to investigate the effect of shear flow on hovering vortex. An in-house fluid solver that is based on immersed boundary method (IBM) is used to study the flow features and variation in aerodynamic forces. The simulations are carried out for various nondimensional rotation rates, axis ratio (AR) of the cylinder, and shear parameter. In shear flow past rotating elliptic cylinder, the negative vortices are sustained for longer distances in the downstream of the cylinder, and due to the velocity gradient, the sequence of the vortex street changes. It also has significant effect on the formation and composition of hovering vortex. To capture these features, each vortex is tracked as they form, detach, and move in the wake of the cylinder. Hovering vortex, formed due to coalescing of multiple vortices near the cylinder, is subdued for smaller rotation rates at moderate shear. It is also observed that lift forces increase linearly with shear, while the frequency of shedding shows no dependency on shear parameter.