Alexander Brady Sharpe was born on August 12, 1827, in Newtown Township, Pennsylvania, to John and Jane Sharpe. He graduated from Jefferson College in 1846, and he was admitted to the bar two years later. He worked as a lawyer in Carlisle, Pennsylvania, and he reportedly “rose to eminence in his profession.” He married Katharine Blaney on December 19, 1854, and the couple apparently had no children. By 1860, he owned $5,000 of real estate and $2,000 of personal property, and he employed at least one white domestic servant.
He enlisted in the Union army on April 21, 1861, and he mustered in as a private in Company A of the 36th Pennsylvania Infantry. He eventually earned a promotion to 2nd lieutenant and then to captain, and he served as an assistant adjutant general. He took part in the siege of Petersburg, and he resigned on January 28, 1865.
He returned to Carlisle after the war and resumed his work as a lawyer. By 1870, he owned $4,000 of real estate and $3,000 of personal property. He died in Carlisle, either of pneumonia or heart failure, on December 25, 1891.