。
She'll probably become a famous artist.
Literal
She [topic-は] future-in famous artist [will become-になる] [probably-だろう].
だろう is the plain-form equivalent of でしょう, expressing the same conjecture. 芸術家 (artist) uses the suffix ~家, which marks someone as a practitioner or professional in a field — 小説家 (novelist), 音楽家 (musician), 政治家 (politician). The な-adjective 有名な modifies 芸術家 directly, forming 'famous artist' as a single noun phrase that then becomes the target of になる.