The adoption of lean-burn technology in modern aero-engines influences the already critical aerothermal conditions at turbine entry, where the absence of dilution holes preserves the swirl component generated by burners and prevents any control on pattern factor. The associated uncertainty and lack of confidence entail the application of wide safety margins in turbine cooling design, with a detrimental effect on engine efficiency. Computational fluid dynamics (CFD) can provide a deeper understanding of the physical phenomena involved in combustor–turbine interaction, especially with hybrid Reynolds-averaged Navier–Stokes (RANS) large eddy simulation (LES) models, such as scale adaptive simulation (SAS), which are proving to overcome the well-known limitations of the RANS approach and be a viable approach to capture the complex flow physics. This paper describes the numerical investigation on a test rig representative of a lean-burn, effusion cooled, annular combustor developed in the EU Project Full Aerothermal Combustor-Turbine interactiOns Research (FACTOR) with the aim of studying combustor–turbine interaction. Results obtained with RANS and SAS were critically compared to experimental data and analyzed to better understand the flow physics, as well as to assess the improvements related to the use of hybrid RANS-LES models. Significant discrepancies are highlighted for RANS in predicting the recirculating region, which has slight influence on the velocity field at the combustor outlet, but affects dramatically mixing and the resulting temperature distribution. The accuracy of the results achieved suggests the exploitation of SAS model with a view to the future inclusion of the nozzle guide vanes in the test rig.