Sheppard was born in about 1736 in Manchester, England, and pursued the trade of a calendar man. This was one of many skills in the highly-developed British textile industry, involving using a hot press to make a smooth finish on cloth. At the age of 26, however, he changed careers and joined the army; September 1776 found him disembarking in America with the 16th (Queen's) Light Dragoons. His experience as a sentry on the night after the Battle of Germantown is described in the previous installment; note that he was 42 years old when he successfully chased down a British light infantryman. When the British army evacuated Philadelphia in June 1778, Sheppard and his regiment returned to New York.
The following year, the 16th Light Dragoons were ordered back to Great Britain. In typical fashion, all of the men who were still fit for foreign service were drafted into other regiments serving in America. 94 men were drafted into the only other British regular cavalry regiment in America, the 17th Light Dragoons; Alexander Sheppard was among them. Soon after, he was in the detachment of the regiment sent on the expedition to Charleston, South Carolina.
We don't know the circumstances, but some time in 1780 Sheppard was injured in such a way as to lose the use of his right hand. On the muster rolls prepared on 4 February 1781, he is listed as having been "Invalided gone to England." Once there, his infirmity along with his long service earned him an out-pension, granted on 10 April 1781 at the age of 45 after 19 years as a soldier.