For many years, a 19th century painting of three white children in a Louisiana landscape held a secret. Beneath a layer of overpaint meant to look like the sky: the figure of an enslaved youth.

Mr. Wiley, famous for his portrait of former President Obama, is now showing paintings of 11 current and former African heads of state. “This is not a celebration of individual leadership,” he said.

This November, Smithsonian’s National Portrait Gallery will celebrate “Portrait of a Nation,” adding four new works to its collection. This year, the honorees are poet Joy Harjo, academic Temple ...