Gib was born in the parish of Muckhart, Perthshire. He studied literature and theology at the University of Edinburgh and at Perth, and was licensed as a preacher in 1740. His eldest brother being a prodigal son, Adam succeeded to the paternal estate, but burned the will when his brother promised to reform. In 1741 he was ordained minister of the large Secession congregation of Bristo Street, Edinburgh. In 1745 he was almost the only Edinburgh minister who continued to preach against rebellion while the troops of Bonnie Prince Charlie were occupying the town. When, in 1747, the Associate Synod, by a narrow majority, decided not to give full immediate effect to a judgment which had been passed in the previous year against the lawfulness of the Burgess Oath, Gib led the protesting minority, who broke off and formed the Antiburgher Synod (April 10) in his own house in Edinburgh.
It was chiefly through Gib's influence that the Antiburghers decided, at subsequent meetings, to summon to the bar their Burgher brethren, and to depose and excommunicate them for contumacy. Gib's action in forming the Antiburgher Synod led, after prolonged litigation, to his exclusion from the building in Bristo Street where his congregation had met. In 1765 he made his response to the General Assembly of the Church of Scotland, which had stigmatized the Secession as threatening the peace of the country. From 1753 till within a short period of his death, he preached regularly in Nicolson Street church, which was constantly filled with an audience of two thousand persons. His dogmatic and fearless attitude in controversy earned for him the nickname "Pope Gib."
Tables for the Four Evangelists (1770, and with author's name, 1800)
The Present Truth, a Display of the Secession Testimony (2 vols., 1774)