We present the detection of an enormous disc of cool neutral hydrogen (HI) gas surrounding the S0 galaxy NGC 612, which hosts one of the nearest powerful radio sources (PKS 0131-36). Using the Australia Telescope Compact Array, we detect M_HI = 1.8 x 10^9 M_sun of HI emission-line gas that is distributed in a 140 kpc wide disc-like structure along the optical disc and dust-lane of NGC 612. The bulk of the gas in the disc appears to be settled in regular rotation with a total velocity range of 850 km/s, although asymmetries in this disc indicate that perturbations are being exerted on part of the gas, possibly by a number of nearby companions. The HI disc in NGC 612 suggests that the total mass enclosed by the system is M_enc ~ 2.9 x 10^12 sin^-2(i) M_sun, implying that this early-type galaxy contains a massive dark matter halo. We also discuss an earlier study by Holt et al. that revealed the presence of a prominent young stellar population at various locations throughout the disc of NGC 612, indicating that this is a rare example of an extended radio source that is hosted by a galaxy with a large-scale star-forming disc. In addition, we map a faint HI bridge along a distance of 400 kpc in between NGC 612 and the gas-rich (M_HI = 8.9 x 10^9 M_sun) barred galaxy NGC 619, indicating that likely an interaction between both systems occurred. From the unusual amounts of HI gas and young stars in this early-type galaxy, in combination with the detection of a faint optical shell and the systems high infra-red luminosity, we argue that either ongoing or past galaxy interactions or a major merger event are a likely mechanism for the triggering of the radio source in NGC 612. This paper is part of an ongoing study to map the large-scale neutral hydrogen properties of nearby radio galaxies. --abridged--