Final answer:
The Beatles performed at The Star-Club in Hamburg during their early years before achieving fame.
Step-by-step explanation:
The Reeperbahn club in which the Beatles performed during their early years in Hamburg is known as the B) The Star-Club.
They played there extensively before they rose to international stardom. These performances were significant in their development as a band, helping them gain the experience and exposure that would contribute to their later success. Hamburg's live music scene at the time was vibrant and played a critical role in shaping the music of the 1960s.