Supercritical (SC) fluid technologies are well-established methods in modern green chemical synthesis. Using SC fluids as solvents instead of traditional liquids gives benefits of higher diffusivity and lower viscosity, which allows mass transfer intensification and, thus, an increased production rate of chemical transformations. Therefore, a conjugation of heterogeneous catalysis with SC media is a large step toward a green chemistry. Tetralin (TL) is an important hydrogen donor solvent used for biomass liquefaction. In industry, TL is obtained via catalytic hydrogenation of naphthalene (NL). Herein, for the first time we have demonstrated the NL hydrogenation with close to 100% selectivity to TL at almost full conversion in the SC hexane. The observed transformation rates in SC hexane were much higher allowing process intensification. The downstream processes can be also facilitated since hexane after depressurisation can be easily separated from the reaction products via simple rectification. The TL synthesis was studied in a batch reactor at variation of reaction temperature and overall pressure. For the first time for this process, low Pt-loaded (1 wt.%) nanoparticles stabilized within hyper-cross-linked aromatic polymer (HAP) were applied. The Pt/HAP catalyst was stable under reaction conditions (250 °C, 6 MPa) allowing its recovery and reuse.