Becoming an act for a cruise ship is a great way to earn money playing your music. Typically, when submitting Set Lists for international performances, the set list is submitted to the Performing Rights Organization in the territory where the performance took place. (Learn how to submit these through your Songtrust account here).
Cruise ships often cross into many different territories on their voyage, so are you supposed to submit each set list to different PRO's depending on where you are at the time of your performance? The answer is NO.
For cruise ships, it’s all based on which PRO licenses the cruise line. So for example, any cruise lines that are based in the United States would be licensed by ASCAP and BMI, regardless of the territories that the ship sails through.
When performing on the ship, the set list should be given to the person responsible for submitting music details to the PRO that is licensing the ship. The PROs receive the set lists from the cruise lines they license and will also chase them for missing data if necessary. In theory, the artists/songwriter should not need to personally submit set lists, as it is the responsibility of the cruise line. If your cruise line is not sending them, then you are still able to submit them personally.