。
She became an actress the following year.
Literal
She [topic-は] that following-year [time-に] actress [become-に] turned-into.
翌年 (よくねん) is the formal, written word for 'the following year' — more concise and bookish than その次の年. 女優 ('actress') uses the gendered suffix 女, mirroring 男優 ('actor'); modern usage is shifting toward gender-neutral 俳優 for both, but 女優 remains the standard term in mainstream media and award categories. The に of 女優になる marks the result of a change of state — the same pattern that powers 大人になる ('become an adult') and 先生になる ('become a teacher'). Note the time に on 翌年, marking 'when' the change happened.