The present-day architecture of planetary systems contains information about their formation and migration histories. The origin of hot Jupiters (HJs; P ≲ 10 d, Rp > 8 R⊕) has long been a matter of debate. While most of them are found to be `lonely', there is a rare population of HJs hosting small inner-orbit companions (eight known as of May 2026). Their peculiar architecture suggests a gentle disc-migration mechanism. In this study, we present the discovery and characterisation of the multi-planet system TOI-1533, comprising an inner sub-Neptune (TOI-1533 b, Porb = 3.63 d, Rp = 3.15 R⊕) and an outer hot giant planet (TOI-1533 c, Porb = 8.06 d, Rp > 7.5 R⊕) with substantial H/He by mass (ρp < 0.48 g cm-3), both transiting an active K-dwarf star (Teff ≈ 5130 K; V (mag) ≈ 11). Our joint modelling of stellar activity and planetary signals from radial velocities (HARPS-N) and transits (TESS) allowed us to detect the planetary Keplerian signals (approximately 10 σ) and isolate the stellar modulation. The inclusion of simultaneous photometry in the multi-dimensional Gaussian processes formalism was a fundamental addition to the spectroscopic activity indicators, enabling the disentanglement of stellar activity from planetary signals. The mass ratio of the two confirmed planets (Mb/Mc about 0.8), together with the super-Neptune mass of the large outer companion (Mc ≈ 40 M⊕), makes this system unusual compared to the other known HJs with low-mass inner companions.