He was educated at Westminster School and privately by Michael Maittaire.
In May of that year he was made genealogist of the newly created Order of the Bath.
This was a new office attached to that of the genealogist and first companion of the order; this creation was the work of his father, who had risen to the post of Garter Principal King of Arms.
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.
The younger Anstis died a bachelor on 5 December 1754 at his house in Mortlake, Surrey, and was buried at Duloe, Cornwall.