The UAV market is currently very competitive, driving the manufacturers to design more efficient solutions to obtain a competitive edge. A cost-effective approach is to improve an existing product 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 aero-structural optimization of the wing is performed using coupled high-fidelity Computational Fluid Dynamics (CFD) and Computational Structural Dynamics (CSD), based on the finite-volume and finite-element methods, respectively. Gradient-based optimization fed with derivatives of functions of interest computed using the adjoint method are used for computational efficiency. First, the design framework is demonstrated for individual discipline problems: CFD-based wing aerodynamic shape optimization for drag minimization at cruise lift condition; and CSM-based wingbox composite structural optimization at high-g load condition with deformation and failure constraints. Then, 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 and chord distributions, span, sweep and airfoil shape using the free-form deformation approach, as well as material thicknesses and carbon fiber orientations. New optimized wing geometries for the different problems are discussed and compared, highlighting the gains obtained using the coupled formulation. While the multidisciplinary solution does not reach the aerodynamic-only discipline minimum drag nor the structural-only discipline minimum mass values, it achieves the coupled, realistic, aerostructural best performance. The results identify possible weaknesses of the current UAV wing, evaluate how the wingbox structural behavior is expected to change and provide meaningful engineering insights for the growth MAME UAV design.