He was educated at Westminster School and was a student of Trinity College, Cambridge in 1646.
He was created Earl of Yarmouth in 1679. He travelled abroad in France. He was knighted on 27 May 1660.
In 1661 Paston was elected Member of Parliament for Castle Rising and sat until 1673, when he had to relinquish his seat on being raised to the peerage as Viscount Yarmouth.
He had inherited the baronetcy on the death of his father in 1663. He was appointed Lord Lieutenant of Norfolk on 6 March 1676, retaining the office until his death.
He was created the 1st Earl of Yarmouth in 1679. Following the creation of the Royal Society in 1660, he was accepted as an Original Fellow on 20 May 1663.
With another Fellow, Thomas Henshaw, he attempted to discover a formula for the fabled "red elixir", another name for the philosopher"s stone which alchemists believed could transmute base metals into gold.
Paston lived at Richmond. There is a painting in the Castle Museum, Norwich of Robert Paston"s belongings, called The Paston Treasure. Paston married Rebecca Clayton daughter of Sir Jasper Clayton, Haberdasher, of London on 15 June 1650.
Rebecca died on 16 February 1694.
Cavalier Parliament. Royal Society]
In 1660 he was elected Member of Parliament (Member of Parliament) for Thetford in the Convention Parliament.