We present multi-frequency observations of the radio galaxy Hydra-A (3C218) located in the core of a massive, X-ray luminous galaxy cluster. IFU spectroscopy is used to trace the kinematics of the ionised and warm molecular hydrogen which are consistent with a ~ 5 kpc rotating disc. Broad, double-peaked lines of CO(2-1), [CII]157 μm and [OI]63 µm are detected. We estimate the mass of the cold gas within the disc to be Mgas= 2.3 ± 0.3 x 109 M⊙. These observations demonstrate that the complex line profiles found in the cold atomic and molecular gas are related to the rotating disc or ring of gas. Finally, Hubble Space Telescope image of the galaxy shows that this gas disc contains a substantial mass of dust. The large gas mass, SFR and kinematics are consistent with the levels of gas cooling from the ICM. We conclude that the cold gas originates from the continual quiescent accumulation of cooled ICM gas. The rotation is in a plane perpendicular to the projected orientation of the radio jets and ICM cavities hinting at a possible connection between the kpc-scale cooling gas and the accretion of material onto the black hole. We discuss the implications of these observations for models of cold accretion, AGN feedback and cooling flows.