Born to an Irish Catholic family, Dempsey took up a military career. As the Penal Laws in existence in Restoration Ireland made it very difficult for Catholics to serve in the Irish Army he instead joined the British Brigade serving in the Portuguese Restoration War between 1662 and 1668. He then transferred into the French Army, serving with Thomas Dongan's Irish Regiment which had been formed by Charles II to fight for his ally Louis XIV of France. He reached the rank of lieutenant colonel.