An oil supply system for supplying oil to a lubricating cavity of a gas turbine engine, the oil supply system has: a de-oiler having a de-oiler air-oil inlet, a de-oiler oil outlet hydraulically connected to the lubricating cavity, and a de-oiler air outlet in fluid flow communication with an environment outside of the oil supply system; and a closed-loop oil circuit including a main pump having a main pump inlet and a main pump outlet, the main pump outlet hydraulically connected to the lubricating cavity, a de-aerator having a de-aerator inlet hydraulically connected to a scavenge outlet of the lubricating cavity, a de-aerator air-oil outlet in fluid flow communication with the de-oiler inlet, and a de-aerator oil outlet hydraulically connected to the main pump inlet.