She grew up to become a famous musician.

Literal

She [topic-は] grew-up [and-て] famous musician became.

成長して connects 'growing up' as the preceding action leading to the result: becoming a famous musician. 有名な (ゆうめいな) means 'famous,' and 音楽家 (おんがくか) means 'musician.' The te-form creates a natural narrative flow: she grew, and as a result, she became famous.