After you have done all that you wished to do at Tacarigua (this includes learning how to sneak and completing the Flotsam side quest, if you are so inclined) you should head out to the pirate-infested island of Tacarigua. This is where you will spend the next significant chunk of the game, as this island is flush with unique quests and side quests, along with tons of new monsters and characters to encounter. Before you can head out, though, you will have to return to Carlos again and speak with him to obtain more information on your upcoming assignment.
You will begin this quest in your room, with a sleeping Patty beside you. If you attempt to speak with her, your avatar will simply say that you had best not disturb her during her slumber. Leave your room and head back into the courtyard. Head into the gate past the training soldiers to find Carlos speaking with Sebastiano in his room. Wait for him to finish talking to Sebastiano and he will brief you. You will have to find the legendary weapon used by the Titans to defeat the Kraken. This will initiate three quests; To Tacarigua, Find Steelbeard, and The Titan Weapon. After you have finished talking with Carlos, head up the stairs to find a bookkeeper named Angus sitting at a desk. Speak with him. He will be calculating the payroll for the Inquisition’s employees. Ask him where your money is, and he will refute you. Apparently word of your split with the Inquisition has already begun to spread. You will have the option to straight up tell him about your involvement in the secret mission, but obviously this is a bad idea. Instead, use the Silver Tongue skill to convince him to slip a little something your way. You will receive 200 gold from Angus.
When you are ready to head out, proceed to the docks. You can find them past the storehouse, out on the pier to the right. Take the gangplank onto the large ship at dock to the left when you are satisfied that you have completed everything that Caldera has to offer. A cutscene will initiate when you board the ship and you will be able to choose whether or not you are ready to disembark. Say yes, and you will be on your way to Tacarigua.