He was tutor to James Geddes, and then about 1727 he became tutor to William Mure of Caldwell, a friend of David Hume. The family passed the winters at Glasgow, where he attended the lectures of Francis Hutcheson. In October 1731 he was licensed to preach by the presbytery of Paisley, where Scottish bookseller Andrew Millar's father, Robert Millar, had also been licensed. By 1745, Andrew Millar was selling Leechman's sermons in London. In 1736 Leechman was ordained minister of Beith in the neighbourhood of Caldwell. He was moderator of a synod at Irvine in 1740, and on 7 April 1741 preached a sermon at Glasgow "on the ... character of a minister of the gospel", which was published, and passed through several editions. In July 1743 he married Bridget Balfour of the Pilrig family, connecting him to her brothers James Balfour and the bookseller John Balfour, and also Robert Whytt and Gavin Hamilton who had married Bridget's sisters. At the end of the year was elected professor of divinity at the University of Glasgow by the casting vote of the lord rector, in a closely contested election with William Craig and John MacLaurin also candidates. He resigned Beith on 3 January 1744 upon his election. The presbytery of Glasgow refused to enrol him, alleging that he had made heretical statements in a sermon published in 1743 "On the Nature, Reasonableness, and Advantages of Prayer". He was accused of laying too little stress upon the merits of the intercession of the Saviour. Hume criticised the sermon in a letter to Leechman's pupil, William Mure, suggesting minute corrections of style, and urging that Leechman really made prayer a mere "rhetorical figure". The synod of Glasgow and Ayr rejected the accusation of the presbytery, and their acquittal was confirmed by the general assembly. Leechman's lectures were popular, and he followed the example first set by Hutcheson of using English instead of Latin. James Wodrow gives a long account of them. They dealt with polemical divinity, the evidences of Christianity, and the composition of sermons. He refused to publish them. He visited England with his old pupil Geddes in 1744, and made the acquaintance of Richard Price. In 1757 he served as Moderator of the General Assembly of the Church of Scotland. In 1759 he went to Bristol in ill-health and drank the waters at Clifton. In 1761 he was appointed Principal of the university at Glasgow, but for a time continued to lecture. He had two paralytic strokes in 1785, and died 3 December in that year.
