。
She grew up to become a veterinarian.
Literal
She [topic-は] grew-up [and-て] veterinarian became.
獣医 (じゅうい) means 'veterinarian' — 獣 (beast/animal) + 医 (doctor). The 成長して...なった pattern captures a life arc: growing up (成長する) followed by the te-form connecting to the outcome (なった). 獣医 is one of the less common professional nouns — Japanese builds many profession words from field + 医/師/家/者: 歯科医 (dentist), 薬剤師 (pharmacist), 音楽家 (musician), 科学者 (scientist).