Eddy-permitting models struggle to simulate accurate Southern Ocean circulation. In particular, the medium resolution Hadley Centre Global Coupled model in CMIP6 exhibits a warm Southern Ocean bias and weak Antarctic Circumpolar Current (ACC) transport. These issues are attributed with a poor representation of mesoscale eddies, which also impair the simulated transport of heat and carbon. To rectify these problems, two momentum closures (harmonic and biharmonic) are implemented in the Nucleus for European Modeling of the Ocean general circulation model: 2D Leith and Quasi-Geostrophic Leith. These Leith closures aim to capture the correct cascades of energy and enstrophy in quasi two-dimensional models. Additionally, the harmonic Leith viscosity coefficients can replace the traditional Gent-McWilliams and Redi diffusivity coefficients. In this work we explore Leith closures in an eddy-resolving channel model and an eddy-permitting forced global ocean sea-ice model, Global Ocean Sea-Ice 9 (GOSI9). The idealised model assesses whether the Leith implementation functions as intended. In the GOSI9 configuration, the harmonic Leith schemes increase the ACC transport by $10-17$\%. This is in response to isopycnal flattening across Drake Passage that reduces a strong Westward flow at $60^{\circ}$S. This increase in ACC transport coincides with reduced warming around the Antarctic Continent. Each harmonic Leith scheme produce polar responses in the North Atlantic, where QG Leith runs display the weakest Atlantic Meridional Overturning Circulation and weakest northward heat transport. Overall, the 2D Leith scheme demonstrates a better response, but further tuning and testing is necessary.