Recent observations have shown that compact nuclear star clusters (NSCs) are present in up to 80 per cent of galaxies. However, detailed studies of their dynamical and chemical properties are confined mainly to spiral galaxy hosts, where they are more easily observed. In this paper, we present our study of the NSC in FCC 277, a nucleated elliptical galaxy in the Fornax cluster. We use a combination of adaptive optics assisted near-infrared integral field spectroscopy, Hubble Space Telescope imaging and literature long-slit data. We show that while the NSC does not appear to rotate within our detection limit of similar to 6 kms(-1), rotation is detected at larger radii, where the isophotes appear to be discy, suggesting the presence of a nuclear disc. We also observe a distinct central velocity dispersion drop that is indicative of a dynamically cold rotating sub-system. Following the results of orbit-based dynamical modelling, corotating as well as counter-rotating stellar orbits are simultaneously needed to reproduce the observed kinematics. We find evidence for varying stellar populations, with the NSC and nuclear disc hosting younger and more metal rich stars than the main body of the galaxy. We argue that gas dissipation and some level of merging have likely played an important role in the formation of the nucleus of this intermediate-mass galaxy. This is in contrast to NSCs in low-mass early-type galaxies, which may have been formed primarily through the infall of star clusters.