Alexander began his career in India when he arrived at Fort St George, Madras, in 1752, at the age of twenty-three, and became a factor there. He was also employed under the Accountant for Madras, and in 1754 became Sub-Accountant and Book-Keeper of Deposits from the Mayor's Courts. He was Sheriff of Madras in 1754 and again in 1757. In the latter year he became Junior Merchant at Madras. In 1759, he was appointed Third in Council at Vizagapatam; in 1760, Senior Merchant and Third in Council at Masulipatam; and in 1762 Eleventh in Council at Fort St George, Civil and Military Paymaster, and Military Storekeeper.