He served as Lord Lieutenant of Bedfordshire from 1621 to 1627 and again from 1629 to his death. From 1621 to 1623, Henry held the title jointly with his father Charles Grey, 7th Earl of Kent. From 1625 to 1627 and again from 1629 to his death, he held the title jointly with Thomas Wentworth, 1st Earl of Cleveland.
He died childless and his primary title as Earl of Kent was inherited by his closest male-line relative, Anthony Grey, 9th Earl of Kent, the Rector of Burbage, Leicestershire. Anthony was a second cousin of his father as they were both great-grandsons of George Grey, 2nd Earl of Kent. His title of Baron Grey de Ruthyn was awarded by the House of Lords to his nephew Charles Longueville, 12th Baron Grey de Ruthyn, son of his sister Susan.