A thorough understanding of the effects of sloshing on aircraft dynamic loads is of great relevance for the future design of flexible aircraft to be able to reduce their structural mass and environmental impact. Indeed, the high vertical accelerations caused by the vibrations of the structure can lead to the fragmentation of the fuel free surface. Fluid impacts on the tank ceiling are potentially a new source of damping for the structure that has hardly been considered before when computing the dynamic loads of the wings. This work aims at applying recently developed reduced-order models of sloshing to the case of a research wing to investigate their effects on the wing aeroelastic response under pre-critical and post-critical conditions. The vertical sloshing dynamics is considered using neural networks trained with experimental data from a scaled tank and then integrated into the aeroelastic system following a suitable scaling procedure. The results concern the aeroelastic response of the wing to gust input under pre-critical (flutter) conditions as well as post-critical conditions highlighting the onset of limit cycle oscillations caused by sloshing, the only nonlinear phenomenon modelled in the present simulation framework. Moreover, the load alleviation performances will be assessed for a typical landing input.