Upvote:3
Cruise ships have an onboard Morgue, that's the answer to the title. But you already knew that!
If you then zoom into the 'What happens to the body?' question. This depends on the decisions made by the Deceased's family in cooperation with the cruise crew.
You (in cooperation with the cruise crew) need to contact a (local, if possible) funeral provider at the first harbor or port you arrive at. Then transport of the body starts, which can be very costly.
You'll probably need to contact a funeral director or a specialized transport company as without experts; you won't get far without expertise here. You might even need to work with 'two' funeral providers.
Not a single person will be buried without consent and communication with the deceased's family.
Source: https://www.funeralwise.com/2019/01/16/shipping-a-dead-body-10-things-you-need-to-know/