Reduced order modelling (ROM) techniques allow to reduce the cost of shape op-timisation problems. In the present work, the compressible turbulent flow around a gas turbine profile is studied by a Discontinuous Galerkin (DG) scheme. The simulations are accelerated by the combination of two existing ROM approaches: Domain Decomposition and Local Proper Orthogonal Decomposition in a DG (LPOD-DG) framework. In particular, the focus is fixed on the airfoil suction side which is deformed while the pressure side remains fixed. The proposed method allows to reduce significantly the number of degrees of freedom in the simulation. The method is evaluated by performing a set of random predictions for shapes not included in the training database and comparing the obtained results with high-fidelity simulations. The approach is also compared to a p-adaptive scheme. Finally, the use of an automatic adaptive technique is investigated in order to improve the prediction accuracy at runtime.