The ice giants Uranus and Neptune are a largely unexplored class of planet that has received only the briefest of glimpses by the Voyager 2 spacecraft. A mission concept for a flagship mission to one of the ice giants includes a NASA-provided spacecraft that would carry and deliver a European probe to the ice giant atmospheric entry interface point, and would subsequently act as a relay receiving station for the atmospheric probe science telemetry. The primary goal of the European ice giant atmospheric probe would be to measure the well-mixed abundances of the ice giant atmosphere, sampling well into the cloud-forming regions of the troposphere where many cosmogenically important and abundant species are expected to be well mixed, far below regions directly accessible to cloud top remote sensing. Throughout the atmospheric descent, the probe would measure pressure and temperature to provide valuable context for the composition measurements, the vertical thermal and energy structure and static stability, the location, density, and composition of the upper cloud layers, as well as direct tracking of the planet's atmospheric dynamics including zonal winds, waves, convection and turbulence.