North Mississippi Allstars return with “What You Gonna Do?,” a funky, revved-up take on the vintage gospel song originally found on the Staple Singers’ 1965 album Freedom Highway.

One of the album’s final tracks, “Long Haired Doney,” nods to the group’s early days, when fellow Mississippi bluesman R.L. Burnside took the young Allstars under his wing. After Burnside ...