In Assassin's Creed III, Providence is the ship commanded by Connor's father, Haytham Kenway. Haytham uses the vessel during the opening chapters as he travels to the American colonies on a mission for the Templar Order.
The ship appears before the game shifts to Connor's perspective and helps establish Haytham as a trained, influential Templar. Its name is easy to overlook because the larger narrative later emphasizes Connor's land missions, frontier travel, and naval activities aboard his own ship.
Connor's vessel is the Aquila, not the Providence. The Jackdaw belongs to Edward Kenway in Black Flag, and the Morrigan belongs to Shay Cormac in Rogue. Haytham's command of the Providence also reflects the game's early maritime setting, linking the Kenway family story to the Atlantic world before the American Revolution becomes central.