Results from the study of the rare decays $ {K}^{+}\to {\pi}^{+}\nu \overline{\nu} $ , K + → π + μ + μ − and K + → π + γγ at the NA62 experiment at CERN are interpreted in terms of improved limits for $ \mathcal{B}\left({K}^{+}\to {\pi}^{+}X\right) $ and coupling parameters of hidden-sector models, where X is a mediator. World-leading limits are achieved for dark photon, dark scalar and axion-like particle models.