The electrical conductivity of high-pressure silicates profoundly influences the interior dynamics of rocky planets. Employing the Kubo-Greenwood formalism, we perform ab initio calculations of electronic conductivity in Fe-bearing post-perovskite under super-Earth mantle conditions, up to 4000 K and 500 GPa. Electronic structures are obtained via many-body perturbation theory, incorporating dynamical screening and correlations among localized Fe-3d orbitals. In contrast to (Fe,Mg)O, for which metallization has been reported at comparable conditions, our results indicate that post-perovskite with Earth-like Fe contents is unlikely to metallize in super-Earth mantles via band-gap closure, yielding negligible low-frequency conductivity. Thus, band conduction is negligible under the conditions examined. Small-polaron hopping is a plausible explanation for the larger measured total conductivity, but testing this hypothesis requires explicit calculations beyond the present band-conduction treatment.