The present work studies the effect of entropy dispersion on the level of combustion noise at the turbine outlet of the Rolls-Royce ANTLE aero-engine. A new model for the decay of entropy waves, based on modelling dispersion effects, is developed and utilised in a low-order network model of the combustor (i.e. LOTAN code that solves the unsteady Euler equations). The proposed model for the dispersion of entropy waves only requires the mean velocity field as an input, obtained by RANS computations of the demonstrator combustor. LOTAN is then coupled with a low order model code (LINEARB) based on the semi-actuator disk model that studies propagation of combustion noise through turbine blades. Thus, by combining LOTAN and LINERAB we predict the combustion noise and its counterparts, direct and indirect noise, generated at the turbine exit. In comparison with experimental data it is found that without the inclusion of entropy dispersion, the level of combustion noise at the turbine exit is over-predicted by almost two orders of magnitude. The introduction of entropy dispersion in LOTAN results in much better agreement with the experimental data, highlighting the importance of entropy wave dispersion for the prediction of combustion noise in real engines. In more detail, the agreement with the experiment for high and low frequencies was very good. At intermediate frequencies the experimental measurements are still over-predicted, however the predicted noise is much smaller compared to the case without entropy dispersion. This discrepancy is attributed to (i) the role of turbulent mixing in the overall decay of the entropy fluctuations inside the combustor, not considered in the model developed for the decay of entropy waves, and (ii) the absence of a proper model in LINEARB for the decay of entropy waves as they pass through the turbine blade rows. These are areas that still need further development to improve the prediction of low-order network codes.