The theory is developed for the convective stability of a rotating spherical shell of fluid upon which is initially imposed a stable thermally induced shear flow. The fluid shell contains heating sources which are distributed proportional to the sine of the polar angle squared. Thus the analysis has a number of similarities to some geophysical flow situations. It is found that the properties of the solution are strongly dependent on the initial conditions. Thus to obtain further insight concerning the stability of the system numerical solutions are obtained at two shell thicknesses. The critical values of the Taylor number ($T$) and the Rayleigh number ($C$) are generally similar to those found in previous studies of rotating fluid shells. However the effect of the initial shear flow is to reduce the critical value of $C$ for a given $T$, below that found for uniform heating and an initially quiescent state. The flows obtained at the onset of instability are toroidal cells which vary in number dependent on $T$ and $C$. A maximum of six cells are found at large values of $T$. A significant effect of the initial shear flow is the occurrence of a rapid change in stability when the number of toroidal cells changes.