heir
A person who will inherit money, property, or a title.
An heir is someone who will receive money, property, or a title when another person dies. If your grandmother leaves you her house in her will, you become the heir to that house. If a king has a daughter who will become queen after him, she is the heir to the throne.
The word comes from an old idea about inheritance: passing valuable things from one generation to the next. In many countries, royal families follow strict rules about who becomes the heir. The oldest child might be first in line, or historically, the oldest son. When someone is called the heir apparent, it means everyone knows they'll inherit unless something very unusual happens.
You might hear someone called an heiress (a feminine form, though heir works for anyone). A person can be the heir to a fortune, a family business, or even just a collection of old photographs. Sometimes people use the word more broadly, like calling someone the heir to a famous musician's style, meaning they carry on that person's legacy or approach.