In 1741 he went to Trinity College, Cambridge, where his elder brother Edward Moises, later vicar of Masham, Yorkshire, was a fellow.
[1][2] Also in 1749, on the recommendation of Edmund Keene, Moises was appointed headmaster of Newcastle Free School, in succession to Richard Dawes.
The school at the time had few pupils, but Moises raised standards, becoming admired for his consistent approach.
In 1750 the corporation of Newcastle raised his salary, and on 21 April 1761 they appointed him to the morning-lectureship of All Saints' Church.
[1] In 1787 Moises was presented to the rectory of Greystoke, Cumberland, and resigned the mastership of the school, after nearly 40 years; he was succeeded by his nephew, the Rev.
[1] Other pupils included: In 1810 a mural monument, executed by John Flaxman, with a Latin inscription composed by Sir William Scott, was erected to Moises in St Mary's porch, St Nicholas's Church.