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 France from 1798–1800. Under the command of Admiral Dmitry Senyavin, he distinguished himself in 1807 in the Battle of Athos and the 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 during the 1813 siege of Danzig.