His eldest son, the eighth Earl, died as a child and was succeeded by his younger brother, the ninth Earl. He was Cofferer of the Household and Lord Lieutenant of Nottinghamshire and Cambridgeshire. He married his first cousin Catherine Pelham (died 1760), daughter and heiress of Henry Pelham. In 1756 his uncle the Duke of Newcastle upon Tyne was created Duke of Newcastle-under-Lyne, with remainder to his nephew Lord Lincoln, and on the Duke's death in 1768 Lincoln succeeded as second Duke of Newcastle-under-Lyne according to the special remainder. He assumed by Royal Licence the additional surname of Pelham the same year.