An axially staged combustion system includes a primary fuel nozzle, a primary combustion zone defined downstream from the primary fuel nozzle, a conical duct disposed downstream from the primary combustion zone and an integrated exit piece disposed downstream from the conical duct. The conical duct and the integrated exit piece at least partially form a hot gas path of the duct section. A plurality of fuel injectors is oriented radially inwardly with respect to an axial centerline of the duct section and is disposed downstream from the primary combustion zone. Each fuel injector of the plurality of fuel injectors provides for injection of a secondary fuel-air mixture into the hot gas path. The plurality of fuel injectors is distributed along at least one of the conical duct and the integrated exit piece.