Context. Small planets transiting bright nearby stars are essential to our understanding of the formation and evolution of exoplanetary systems. However, few constitute prime targets for atmospheric characterization, and even fewer are part of multiple star systems. Aims. This work aims to validate TOI-4336 A b, a sub-Neptune-sized exoplanet candidate identified by the TESS space-based transit survey around a nearby M dwarf. Methods. We validated the planetary nature of TOI-4336 A b through the global analysis of TESS and follow-up multi-band high-precision photometric data from ground-based telescopes, medium- and high-resolution spectroscopy of the host star, high-resolution speckle imaging, and archival images. Results. The newly discovered exoplanet TOI-4336 A b has a radius of 2.1 ± 0.1 R ⊕ . Its host star is an M3.5-dwarf star with a mass of 0.33 ± 0.01 M ⊙ and a radius of 0.33 ± 0.02 R ⊙ , and is a member of a hierarchical triple M-dwarf system 22 pc away from the Sun. The planet’s orbital period of 16.3 days places it at the inner edge of the habitable zone of its host star, which is the brightest of the inner binary pair. The parameters of the system make TOI-4336 A b an extremely promising target for the detailed atmospheric characterization of a temperate sub-Neptune by transit transmission spectroscopy with JWST.Read less <