A multiterminal device based on a carbon nanotube quantum dot was used at very low temperature to probe a single electronic and nuclear spin embedded in a bis-(phthalocyaninato) terbium (III) complex (TbPc${}_{2}$). A spin-valve signature with large conductance jumps was found when two molecules were strongly coupled to the nanotube. The application of a transverse field separated the magnetic signal of both molecules and enabled single-shot read-out of the terbium nuclear spin. The Landau-Zener (LZ) quantum tunneling probability was studied as a function of field sweep rate, establishing a good agreement with the LZ equation and yielding the tunnel splitting $\ensuremath{\Delta}$. It was found that $\ensuremath{\Delta}$ increased linearly as a function of the transverse field. These studies are an essential prerequisite for the coherent manipulation of a single nuclear spin in TbPc${}_{2}$.