Stringent regulations of pollutant emissions now apply to new-generation combustion devices. To achieve low nitrogen oxides (NOx) and carbon monoxide (CO) emissions simultaneously, a complex optimisation process is required in the development of new concepts for engines. Already efficient for the prediction of turbulent combustion, Large Eddy Simulation (LES) is also a promising tool to better understand the processes of pollutant formation in gas turbine conditions and to provide their quantitative prediction at the design stage. In this work, a new methodology for the prediction with LES of NOx and CO in realistic industrial configurations is developed. It is based on a new strategy for the description of chemistry, using Analytically Reduced Chemistry (ARC) combined with the Thickened Flame model (TFLES). An ARC with accurate CO and NO prediction is derived, validated on canonical laminar flames and implemented in the LES solver. The accuracy of this approach is demonstrated with a highly resolved simulation of the academic turbulent Sandia flame D, for which excellent prediction of NO and CO is obtained. The methodology is then applied to two industrial configurations. The first one is the SGT-100, a lean partially-premixed gas turbine model combustor studied experimentally at DLR. LES of this configuration highlights the chemical processes of pollutant formation and provides qualitative and quantitative understanding of the impact of the operating conditions. The second target configuration corresponds to a mono-sector prototype of an ultralow NOx, staged multipoint injection aeronautical combustor developed in the framework of the LEMCOTEC European project and studied experimentally at ONERA. An ARC for the combustion of a representative jet fuel surrogate is derived and used in the LES of the combustor with an Eulerian formalism to describe the liquid dispersed phase. Results show the excellent performances of the ARC, for both the flame characteristics and the prediction of pollutants.