Next month, New York City will begin cleaning up unearthed human remains and restoring the damaged sea wall along the shoreline of Hart Island, which is one of the largest public cemeteries in the country.

The restoration comes seven years after superstorm Sandy in 2012, when 8-foot-high floodwaters swept over the island and heavily eroded the shoreline. The battering exposed remains from interments performed along the island’s north shore throughout the 20th century.

“It’s...