Given the stringent emission regulations of aircraft engines, the trend in the aero industry is toward developing leaner combustion systems, which are prone to produce combustion instabilities. Hybrid methods of simultaneous acoustics and fluid dynamics simulations offer an elegant solution for the numerical prediction of these instabilities, taking advantage of the appropriate discretization of relevant scales. The presented work employed a hybrid simulation framework to identify the thermoacoustic response of a practically relevant configuration. The fluid dynamics were described using a computational fluid dynamics solver employing the low Mach formulation of the Navier–Stokes equations, while the acoustics were simulated using a computational aeroacoustics solver employing the acoustic perturbation equations. The coupling was implemented to exchange information between both solvers during runtime. The considered real-life configuration was designed to investigate the thermoacoustic behavior of realistic gas turbine injectors. It is acoustically excited to characterize the given injector via the flame transfer function approach under controlled operating conditions. The computational fluid dynamics simulation results were postprocessed to obtain the acoustic behavior of the combustor. The reacting scattering matrix was constructed and then compared to the experimental reference, both obtained using the multimicrophone method. Finally, two different postprocessing approaches were used to calculate the flame transfer function and discuss the applied hybrid computation method. This work demonstrated that the hybrid method can capture general features of the flame response of a complex three-dimensional combustion system.