At the age of fourteen he appears to have been employed as secretary to the Society for Promoting Constitutional Information, a radical association which numbered Sir William Jones (1746–1794) among its members, but he can have held this post only a short time.
Though he worked for many years at this translation, and received encouragement from the continent as well as in England, the only portion of it ever published was a specimen which appeared in the third annual report of the London Jews' Society.
From about 1808 to 1815 Yeates was employed by Claudius Buchanan to catalogue and describe his oriental manuscripts brought from India; and for much of this period he lived in Cambridge, where the University Press published (1812) his 'Collation of an India Copy of the Pentateuch;' the copies of this work were presented by the press to Yeates.
He also, through Buchanan, obtained employment from the Bible Society, and superintended their editions of the Æthiopic Psalter and the Syriac New Testament.
The same year he produced a 'Variation Chart of all the Navigable Oceans and Seas between latitude 60 degrees N. and S. from Documents, and delineated on a new plan;' and in 1819 a Syriac grammar, the first that ever appeared in English.