Archibald had already been created Lord Primrose and Dalmeny and Viscount of Rosebery in 1700, with remainder to his issue male and female successively, and in default thereof to the heirs of entail in the lands of Rosebery, and was made Lord Dalmeny and Viscount of Inverkeithing at the same time as he was given the earldom (and with similar remainders).

His son, Neil Primrose, the third Earl, sat in the House of Lords as a Scottish representative peer from 1768 to 1784.

He represented Helston and Cashel in the House of Commons of the United Kingdom and served as Lord Lieutenant of Linlithgowshire.

Their eldest son, Albert Edward Harry Primrose, the sixth Earl, represented Midlothian in Parliament from 1906 to 1910 but then did not take an active part in politics until the 1940s, when he served in Winston Churchill's 1945 caretaker government as Secretary of State for Scotland.

The heir apparent is the Earl's son, Albert Caspian Harry Primrose, Lord Dalmeny (born 2005).