* If you mean the house where a princess lives: It's simply "the princess's house" The apostrophe 's' shows possession.
* If you mean a house that is specifically designed for princesses: It could be "the Princess House" (with "Princess" capitalized, as it's a proper noun). This could refer to a specific building or a type of house designed for princesses.
Please provide more context so I can give you the most accurate answer!