Stock is the son of Luke and Ann Stock. He is educated at Mr. Gast’s school in his native city and at Trinity College, Dublin. He obtains a scholarship in 1759, graduates B.A. in 1761, and gains a fellowship in 1763. Having taken orders, Stock retires on the college living of Conwall in the diocese of Raphoe.
Stock is a classical scholar, a linguist, and a man of general culture. In 1776 he publishes anonymously a life of George Berkeley, subsequently republished in the Biographia Britannica, the only memoir on Berkeley based on contemporary information.
In 1793 Stock is collated prebendary of Lismore, but resigns this preferment in 1795, on his appointment to the head-mastership of Portora Royal School. In January 1798 he succeeds John Porter as Bishop of Killala and Achonry. Shortly after his consecration, and while holding his first visitation at the castle of Killala, the bishop becomes a prisoner of the French army under General Jean Joseph Amable Humbert, when French forces land in support of the Irish Rebellion of 1798. Of his experiences as a prisoner of the French he leaves a partial record in his private diary — August 23 to September 15, 1798 — which is printed in William Hamilton Maxwell‘s History of the Rebellion of 1798, and in two letters to his brother Stephen, published in the Auckland Correspondence.
In 1799 Stock publishes a more complete account of the French invasion of County Mayo in his Narrative of what passed at Killala in the Summer of 1798. By an Eyewitness. The impartiality of this work is said to have been a bar to the bishop’s advancement. He also writes The Book of the Prophet Isaiah in Hebrew and English, with Notes (Bath, 1803) and The Book of Job metrically arranged and newly translated into English, with Notes (Bath, 1805).
Stock also publishes school editions of Tacitus and Demosthenes, and is an active contributor to the controversial theology of his day. He leaves two manuscript volumes of correspondence which are preserved in the library of Trinity College, Dublin. They consist chiefly of letters written from Killala and Waterford between 1806 and 1813 to his son Henry in Dublin.
In 1810 Stock is translated to the diocese of Waterford and Lismore, and dies at Waterford on August 13, 1813.