<p>We derive new necessary and sufficient conditions for strict efficiency in vector optimization problems for non-smooth mappings. Unlike other approaches, our conditions are described in terms of a suitable directional curvature functional that allows us to derive no-gap second-order optimality conditions in an abstract setting. Our approach allows us to apply our results even when classical assumptions such as the second-order regularity conditions to the feasible set fail, extending the applicability of our approach. As applications to mathematical programming, we provide new primal and dual Karush-Kuhn-Tucker (KKT) second-order necessary and sufficient conditions. We provide some examples to illustrate our findings.</p>