der Kronprinz
crown prince
The official male heir to the throne in a monarchy.
Der Kronprinz wird eines Tages die Nachfolge seines Vaters, des Königs, antreten.
The crown prince will one day succeed his father, the king.

crown prince
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crown prince
The official male heir to the throne in a monarchy.
Der Kronprinz wird eines Tages die Nachfolge seines Vaters, des Königs, antreten.
The crown prince will one day succeed his father, the king.

The word is a simple compound of 'die Krone' (the crown) and 'der Prinz' (the prince). So it literally refers to the prince who will inherit the crown.
Der junge Kronprinz wurde auf seine zukünftigen Aufgaben als Herrscher vorbereitet.
The young crown prince was prepared for his future duties as ruler.
You can recognize the figurative meaning from the context. If the sentence is about a 'Unternehmen' (company), a 'Partei' (party), or an 'Organisation' (organization), it means the designated successor. If it is about a 'König' (king), 'Thron' (throne), or 'Monarchie' (monarchy), it means the actual heir to the throne.
In der Firma gilt der Sohn des Chefs als Kronprinz und zukünftiger Leiter.
In the company, the boss's son is considered the heir apparent and future director.
In the figurative meaning, a person is often not directly called a 'Kronprinz' (crown prince/heir apparent), but the idea is expressed indirectly. Typical formulations are 'als Kronprinz gelten' (to be considered the heir apparent) or 'als Kronprinz gehandelt werden' (to be talked about as the heir apparent).
Er wird schon seit Jahren als Kronprinz für den Parteivorsitz gehandelt.
For years, he has been talked about as the heir apparent for the party leadership.
successor
'der Nachfolger' and 'der Kronprinz' can both refer to a person who is expected to take over an important position later. 'Nachfolger' is the general word: it works for offices, jobs, functions, and also for a line of succession. 'Kronprinz' is much more specific. Strictly speaking, it means the male heir to the throne in a monarchy. In a figurative sense, people sometimes also use it for a person in a company or organization when that person is clearly seen as the future boss or leader. Learners may confuse the words because both express a future takeover. 'Nachfolger' is the safer choice when you are not talking about a monarchy or using a deliberately figurative expression.

In der Firma gilt Mehmet als Kronprinz des Geschäftsführers.
In the company, Mehmet is seen as the managing director's heir apparent.
Nach dem Rücktritt des Trainers hat der Verein schnell einen Nachfolger gefunden.
After the coach resigned, the club quickly found a successor.