He was educated at Westminster School and privately by Michael Maittaire. He graduated from Corpus Christi College, Oxford, in 1725.
In May of that year he was made genealogist of the newly created Order of the Bath. On 6 October 1727, he was appointed Blanc Coursier Herald. In 1736 he was made a fellow of the Society of Antiquaries of London and he became the sole Garter King of Arms on his father"s death in 1744.
In 1749, he became a barrister of the Middle Temple, although he never practised law.
The younger Anstis died a bachelor on 5 December 1754 at his house in Mortlake, Surrey, and was buried at Duloe, Cornwall.