An analytical approach is adopted to investigate the SH waves in a composite structure consisting of initially stressed rotating piezoelectric layer and initially stressed substrate with rotation. The interface between the layer and the substrate is assumed to be imperfect. Two distinct types of imperfect interfaces (dielectrically weakly and highly conducting) are considered. Secular equations have been obtained for both electrically open and short cases with weakly and highly performing interface. Particular cases have been derived and matched with existing result. The characteristics of SH wave through the considered framework and their state of relying on different physical and geometrical parameters have been scrutinized based on their numerical results. The parallel simulated outcomes of disparate physical quantities, namely, phase velocity, group velocity, dispersive curves, initial stress, rotation and electromechanical coupling factor, and stress distribution of SH wave in the considered structure are investigated. The considered model may be useful in theoretical foundation and practical application for the development of piezoelectric sensors, structural health monitoring, and surface acoustic wave devices.