The UAV market is currently very populated, driving the manufacturers to design more efficient solutions to obtain a competitive edge. A cost-effective approach is to improve existing products using new technologies and design tools. This work addresses the desire of a UAV manufacturer to develop a growth version of an existing Medium-Altitude Medium-Endurance (MAME) Unmanned Aerial Vehicle (UAV). To that end, the aerostructural optimization of the wing is performed using coupled high-fidelity Computational Fluid Dynamics (CFD) and Computational Structural Dynamics (CSD). Gradient-based optimization fed with derivatives of functions of interest computed using the adjoint method are used for computational efficiency. The coupled problem is posed in the aerostructural optimization framework, targeting for maximum aircraft range, being the solution a result of the concurrent discipline analyses. The set of design variables include wing twist distribution, using the free-form deformation approach, material thicknesses and carbon fibre orientations. The optimized wing geometry exhibits a gain of 5\% in aircraft range, with 2\% better aerodynamic efficiency (L/D) and 63\% wing weight reduction. The impact of multilayer composite manufacturing constraints, namely adjacency of ply angles in neighbouring regions and the orthogonality between ply angles, was found not to be significant. The studies identified weaknesses of the baseline wing and provided meaningful engineering insights for the next generation MAME UAV design.