Original: He served as the nominal head of government from 1742 until his death in 1743, but was merely a figurehead for the true leader of the government, Lord Carteret, the Secretary of State for the Northern Department.
Simplified: Wilmington served as the head of government from 1742 until his death in 1743, but was a leader in name only. The true leader of the government was Lord Carteret, the Secretary of State for the Northern Department.