STE-QUEST is a fundamental science mission which is considered for launch within the Cosmic Vision programme of the European Space Agency (ESA). Its main scientific objectives relate to probing various aspects of Einstein's theory of general relativity by measuring the gravitational red-shift of the earth, the moon and the sun as well as testing the weak equivalence principle to unprecedented accuracy. In order to perform the measurements, the system features a spacecraft equipped with two complex instruments, an atomic clock and an atom interferometer, a ground-segment encompassing several ground-terminals collocated with the best available ground atomic clocks, and clock comparison between space and ground via microwave and optical links. The baseline orbit is highly eccentric and exhibits strong variations of incident solar flux, which poses challenges for thermal and power subsystems in addition to the difficulties encountered by precise-orbit-determination at high altitudes. The mission assessment and definition phase (Phase-A) has recently been completed and this paper gives a concise overview over some system level results.