Gas turbine engines with high operational flexibility represent an important area of research. In support of this, the stage change of NOx emissions at high-temperature, full-load conditions are the main target of this research study. To overcome the challenge of decreasing the residence time of hot exhaust gas in the burner, the approach of axial-staged combustion has been used, which aims to burn at lean conditions. A main combustion stage with a conventional burner is followed by a jet-in-crossflow (JIC) stage downstream. This second combustion stage, the test section, burns well over a third of the total fuel amount, which is added by a jet inlet. The entire combustor is designed to run at a pressure of 5 bar, featuring a challenging point of experimental operation. Hence, a steady Computational Fluid Dynamics (CFD) model was created in Star-CCM+ to analyze the JIC stage. A structured mesh grid with local refinement domains was used along with RANS equations, Realizable k-ε turbulence, Complex Chemistry model with Laminar Flame Concept (LFC) applied. The findings of the computational model include a detailed description of the flow field, focusing on vortex formation and penetration depth. Three vortex types and local pressure losses in the shear domain were identified. Results were compared with similar data from literature and a very good match was proven. Optical laser diagnostics should work well to capture the predicted flow penetration. The highest local reaction rates were observed inside a thin flame front between 4 and 6 diameters downstream of the jet. The jet showed a limited expansion into the available channel domain, resulting in a low total heat release and a methane conversion of 52%. Along with production of just under 1% CO, the potential of axial-staged combustion has been outlined by two boundary cases, using either equilibrium main burner stage NOx, which showed a reduction of high incoming NOx, or setting incoming NOx fractions to zero, which yielded a total production of only 17 ppm NOx in the JIC stage.