Spens was the first to translate Plato's Republic into English, printed in quarto at Glasgow by Robert and Andrew Foulis in 1763. The work is dedicated to John Stuart, Third Earl of Bute, during his brief stint as Prime Minister of the United Kingdom before scandal concerning the Seven Years' War ousted him from office. Bute was deeply integrated into the system of patronage surrounding academic appointments in the Scottish university system; the dedication may have been made to help Spens' brother Robert accede to the Chair of Oriental Languages at Glasgow, a bid which was ultimately unsuccessful.

Spens provides no interlinear or running commentary on his translation, but prefaces the work with a "Discourse concerning the philosophy of the ancients," as it is referred to in the book's full title. In it, he provides historical and biographical background to the Republic, and praises it for its agreeable harmony with eighteenth-century Scottish society and religion. Spens does not address his translational method or sources, but a throwaway line alluding to the "Greek of Ficino" suggests that he used Edmund Massey's 1713 edition of The Republic, a facing-page Greek/Latin edition that combined the Greek text and commentary of Henri Estienne (Henricus Stephanus) with the Latin translation by Renaissance Humanist Marsilio Ficino.

The 1763 Republic does not appear to have sold well. It was put on sale for 10s 6d and an audit of the Foulis Press's stock following its financial dissolution under Andrew Foulis the Younger revealed approximately sixty unsold copies. It never received a second edition during the eighteenth century, but it was reprinted with slight emendations in 1804's Works of Plato, translated by Thomas Taylor and Floyer Sydenham. In 1906, it was printed by J.M. Dent and Sons as part of their Everyman's Library line of classical texts. Spens' preface was replaced by a brief introduction to the text and a biography of the translator penned by editor E.P. Dutton. This reprinting received multiple editions in Britain and the United States until the 1920s, when the Everyman's Library replaced it with A.D. Lindsay's 1907 translation, which remains in print to this day.