The nuclear equation of state, which determines the structure and properties of neutron stars, remains subject to substantial theoretical uncertainties, leading to model dependence in predicted observables. Universal relations have emerged as a powerful tool to mitigate this dependence by linking neutron star observables in a framework-independent manner. In this work, we introduce a new universal relation that bridges finite nuclei and neutron stars through the dimensionless quantity zeta=beta 1.4L-1, which couples the compactness of a 1.4M circle dot neutron star to the slope of the nuclear symmetry energy at saturation. The relation is examined under a broad set of relativistic energy density functionals with point-coupling and meson-exchange interactions, as well as nonrelativistic Skyrme functionals. We demonstrate that zeta exhibits a strong exponential correlation with the electric dipole polarizability alpha D in finite nuclei across all considered equations of state. By exploiting experimental alpha D data for selected neutron-rich nuclei, we constrain zeta and translate these constraints into equation-of-state independent bounds on the neutron star radius R1.4 and the symmetry-energy slope L, providing insights into the properties of neutron star matter.