Although representing drastically different chemical natures and types of interactions, the similarity of shape anisotropy of the constituents has created much interest in composites of calamitic liquid crystals (LCs) and carbon nanotubes (CNTs). Despite significant volume of studies on the physical properties of such composites, influence of CNTs on the celebrated re-entrant phenomenon in LCs has not been studied. We report here that a small concentration of CNTs doped to a "nematic mesophase-only" material not only induces the layered smectic A mesophase but also leads to the nematic-smectic-nematic re-entrant sequence as well, demonstrating the delicate interplay between the two entities. To explain this unusual observation, we propose nanophase segregation of the CNT as a possible mechanism. A combination of Flory-Huggins theory and Landau-de Gennes theory has also been provided supporting the observed feature.