G. Mantovan, V. Nascimbeni, S. Desidera, L. Malavolta, J. J. Lissauer, P. Leonardi, T. Azevedo Silva, C. Guerra, D. Polychroni, L. Borsato, M. Baratella, K. Biazzo, D. Nardiello, K. A. Collins, M. Damasso, J. De Leon, M. E. Everett, D. Gandolfi, S. Giacalone, L. Naponiello, G. Piotto, G. Scandariato, K. Stassun, S. W. Yee, L. Affer, F. Amadori, A. Bignamini, S. Colombo, M. D'Arpa, C. D. Dressing, A. Fukui, A. Ghedina, J. Higuera, K. Ikuta, Kawauchi, J. Korth, V. Lorenzi, L. Mancini, M. Mori, F. Murgas, N. Narita, E. Palle, H. Parviainen, A. Ruggieri, A. Savel, R. P. Schwarz, A. Shporer, G. Srdoc, Stockdale, D. Watanabe, R. Zambelli, T. Zingales

The present-day architecture of planetary systems contains information about their formation and migration histories. The origin of hot Jupiters (HJs, P $\lesssim$ 10 d, $R_{\rm p} > 8 R_\oplus$) 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 companions on inner orbits (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, $P_{\rm orb} = 3.63$ d, $R_{\rm p} = 3.15 R_\oplus$) and an outer hot giant planet (TOI-1533 c, $P_{\rm orb} = 8.06$ d, $R_{\rm p} > 7.5 R_\oplus$) with substantial H/He by mass ($ρ_{\rm p} < 0.48$ g cm$^{-3}$), both transiting an active K-dwarf star ($T_{\rm eff} \approx$ 5130 K; $V$ (mag) $\approx$ 11). Our joint modelling of stellar activity and planetary signals from radial velocities (HARPS-N) and transits (TESS) allows us to detect their Keplerian signals (approximately $10~σ$) and to 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 ($M_{\rm b} / M_{\rm c}$ about 0.8), together with the super-Neptune mass of the large outer companion ($M_{\rm c} \approx 40 M_\oplus$), makes this system unusual compared to the other few HJs with low-mass inner companions.