Context. The TESS mission is searching for transiting planets over the entire sky, including two continuous viewing zones. Data from the continuous viewing zones span a long time baseline and offer ideal conditions for precise planet radius estimations, enabling the community to prepare for the PLATO mission. Aims. We report on the validation and characterisation of two transiting planets around TOI-1453, a K-dwarf star in the TESS northern continuous viewing zone. Methods. In addition to the TESS data, we used ground-based photometric, spectroscopic, and high-resolution imaging follow-up observations to validate the two planets. We obtained 100 HARPS-N high-resolution spectra over two seasons and used them together with the TESS light curve to constrain the mass, radius, and orbit of each planet. Results. TOI-1453 b is a super-Earth with an orbital period of Pb=4.314 days, a radius of Rb=1.17±0.06R⊕, and a mass lower than 2.32 M⊕ (99%). TOI-1453 c is a sub-Neptune with a period of Pc =6.589 days, radius of Rc=2.22±0.09 R⊕, and mass of Mc=2.95‑0.84+0.83 M⊕. The two planets orbit TOI-1453 with a period ratio close to 3/2, although they are not in a mean motion resonance (MMR) state. We did not detect any transit timing variations in our attempt to further constrain the planet masses. TOI-1453 c has a very low bulk density and is one of the least massive sub-Neptunes discovered to date. It is compatible with having either a water-rich composition or a rocky core surrounded by a thick H/He atmosphere. However, we set constraints on the water mass fraction in the envelope according to either a water-rich or water-poor formation scenario. The star TOI-1453 belongs to the Galactic thin disc based on Gaia kinematics and has a sub-solar metallicity. This system is orbited by a fainter stellar companion at a projected distance of ∼150 AU, classifying TOI-1453 b and c of S-type planets. These various planetary and stellar characteristics make TOI-1453 a valuable system for understanding the origin of super-Earths and sub-Neptunes.