He studied at the High School of Edinburgh under the Rector Adam from 1783 to 1785, and then served as a volunteer on board H.M.S. Culloden, under Admiral Trowbridge. Greig started his career in the British Royal Navy, serving in East India and Europe from 1785 to 1796. He returned to Russia to take part in the Mediterranean expeditions against Revolutionary France in 1798-1800. Under command of Dmitry Senyavin, he distinguished himself in 1807 in the Battle of Athos and Battle of the Dardanelles, which resulted in the Russian occupation of Lemnos and Tenedos. At the close of the Napoleonic Wars, he was placed in command of the sea blockade of Danzig. When he was a Captain, he and another Scotsman Captain Brown, were involved in some trouble by the wreck of the Imperial frigate Archangel i