The design optimization of aviation propulsion systems by means of computational fluid dynamics is key to increase their efficiency and reduce pollutant and noise emissions. The recurrent increase in available computing power allows nowadays to perform unsteady high-fidelity computations of the different components of a gas turbine. However, these simulations are often made independently of each other and they only share average quantities at interfaces. In this work, the methodology and first results for a sectoral large-eddy simulation of an integrated high-pressure compressor and combustion chamber of a typical turbine engine architecture is proposed. In the simulation, the compressor is composed of one main blade and one splitter blade, two radial diffuser vanes and six axial diffuser vanes. The combustion chamber is composed of the contouring casing, the flame-tube and a T-shaped vaporizer. This integrated computation considers a good trade-off between accuracy of the simulation and affordable CPU cost. Results are compared between the stand-alone combustion chamber simulation and the integrated one in terms of global, integral and average quantities. It is shown that pressure perturbations generated by the interaction of the impeller blades with the diffuser vanes are propagated through the axial diffuser and enter the combustion chamber through the dilution holes and the vaporizer. Due to the high amplitude of the pressure perturbations, several variables are perturbed at the blade-passing frequency and multiples. This is also reflected on combustion where two broadband peaks appear for the global heat release.