Port Royal: The Adventure Begins...

From BoardGameGeek:

Raise the anchors and set sail as Port Royal: The Adventure Begins... introduces a campaign mode to Port Royal. At the beginning of the game, someone reads the prologue of the scenario to be played, then before the start of each turn, players reveal order cards from an event deck that might require the collection of certain crew members or trade with certain ships; players might receive a bonus for certain actions during the turn. Order cards have a time limit, however, after which new cards are played from the event deck, and the end of a scenario depends on which orders have been executed. Port Royal: The Adventure Begins... can be played either competitively or cooperatively.