The dielectric properties of nanocomposites of polystyrene-b-poly (ethylene-co-butylene)-b-polystyrene (SEBS) triblock copolymers containing organically modified clay nanoparticles featuring controlled spatial orientation at the nanoscale: isotropic, totally oriented and partially oriented, have been investigated and correlated with the nanocomposite morphologies. A slow dielectric relaxation process attributed to elastomer chains with reduced mobility confined at nanoparticle/polymer interphase was observed in all the nanocomposites and was found to be dependent on the orientation of nanoclay and polystyrene (PS) domains, the location of clay tactoids as well as the PS block fraction. A dielectric “interfacial” glass transition temperature Tgi assigned to this characteristic relaxation was estimated to occur at temperatures ranging between 6 °C and 35 °C depending on the nanocomposite, which is much higher than the bulk rubber phase glass transition temperature, normally lower than −40 °C for the studied block copolymers. Interestingly, the highest Tgi were associated with the nanocomposites featuring random or partial orientation and/or selective location of nanoparticles in the rubber phase.