Second son of Henry Frederick Howard, third Earl of Arundel and Lady Elizabeth Stuart, was educated abroad, as a Catholic. In 1660 he went as ambassador extraordinary to Morocco. In 1677 he succeeded his brother as duke, having previously been made hereditary earl-marshal. During the Commonwealth and Protectorate he lived in total seclusion. In January, 1678, he took his seat in the House of Lords, but in August the first development of the Titus Oates Plot was followed by an Act for disabling Catholics from sitting in either house of Parliament. He would not comply with the oath and, suspected of doubtful loyalty, withdrew to Bruges for three years. There he built a house attached to a Franciscan convent and enjoyed freedom of worship and scope for his munificence. He was a man of benevolent disposition and gave away the greater part of his splendid library, and grounds and rooms to the Royal Society, and the Arundelian marbles to Oxford University. Jealous of the family honour, he compounded a debt of £200,000 contracted by his grandfather.
The Wikipedia entry for this duke includes more detail about his reaction to the Popish Plot and the Test Acts, because he remained in the House of Lords
He died on January 13, 1684 and was succeeded by his son Thomas by his first marriage to Anne Somerset--he married his mistress Jane Bickerton in 1676 or 1677. More information about his second marriage here.