Abstract: High refractive index dielectric nanoantennas are expected to become key elements for nonlinear nano-optics applications due to their large nonlinearities, low energy losses, and ability to produce high electric field enhancements in relatively large nanoscale volumes. In this work, we show that the nonlinear response from a high-index dielectric nanoantenna can be significantly improved by adding a metallic component to build a metal?dielectric hybrid nanostructure. We demonstrate that the plasmonic resonance of a Au nanoring can boost the anapole mode supported by a Si nanodisk, strongly enhancing the electric field inside the large third-order susceptibility dielectric. As a result, a high third harmonic conversion efficiency, which reaches 0.007% at a third harmonic wavelength of 440 nm, is obtained. In addition, by suitably modifying geometrical parameters of the hybrid nanoantenna, we tune the enhanced third harmonic emission throughout the optical regime. Coupling metallic and dielectric nanoantennas to expand the potential of subwavelength structures opens new paths for efficient nonlinear optical effects in the visible range on the nanoscale.