Fixed-geometry wings on commercial transport aircraft are a compromise: an airfoil optimised for a single cruise point operates off-design for most of a flight as weight falls with fuel burn and as altitude, speed, and payload vary. Morphing trailing edges—continuous, gapless, variable-camber surfaces that replace or augment conventional hinged flaps—offer a route to restore near-optimal lift distribution across the mission. This paper presents an aerostructural optimisation study of an adaptive trailing edge (ATE) applied to a single-aisle, A320-class transport wing. A parametric camber-morphing device occupying the aft 25% of chord over the outer 60% of semi-span is optimised using a Reynolds-Averaged Navier–Stokes (RANS) solver coupled to a genetic-algorithm outer loop and a gradient-based refinement stage, with a structural feasibility constraint imposed through a reduced fluid–structure interaction (FSI) model. At the nominal cruise condition (M = 0.78, altitude 11 278 m, C_L = 0.51), the optimised morphing schedule reduces cruise drag by 3.6% relative to the fixed baseline; integrated over a representative 3 000 km mission with continuous camber scheduling, block-fuel burn falls by 4.1%. Additional benefits in manoeuvre and gust load alleviation—up to 11% root bending moment reduction—are quantified and translated into a notional structural weight credit. The results are consistent with the ranges reported by the NASA/FlexSys ACTE flight programme and the EU SARISTU Adaptive Trailing Edge Device, and they clarify where the largest efficiency gains originate: continuous spanwise lift tailoring rather than local section camber alone.