、。
She succeeded as a singer and became famous.
Literal
She [topic-は] singer [as-として] succeed-and, famous became.
The conjunctive ~し chains two predicates: literally 'X-し, Y' = 'did X, and (then/also) did Y.' It's slightly more written or literary than the everyday ~て chaining and is frequent in narratives that want to give the conjoined actions a touch more weight. Inside the chain, 成功し is the conjunctive form of 成功する ('succeed'); after the comma comes 有名になった ('became famous'), pairing 有名 with the standard Nになる pattern. A tidy biographical sketch in one sentence.