Belasyse graduated from Christ's College, Cambridge in 1667, before a period spent at legal school in the Middle Temple, then considered part of a gentleman's education. In 1674, he raised a company of men for the Scots Brigade, a mercenary unit in the Dutch States Army, whose origins went back to the 1580s, which normally contained three Scots and three English regiments. The latter were withdrawn in 1672 when England allied with France in the 1672-1678 Franco-Dutch War but restored after the 1674 Treaty of Westminster ended their involvement. Henry's company was recruited for one of the restored English regiments, which eventually became the 6th Foot.