。
She grew into a slender young woman.
Literal
She [topic-は] came-of-age [and-て] slender daughter became.
成人して means 'after coming of age / after maturing.' ほっそりした means 'slender' or 'slim' — a 擬態語-derived adjective describing an elegant thinness. ほっそり is one of many Japanese words for types of thinness, each with different nuance: ほっそり (elegantly slim), ほそい (thin), やせている (skinny), スリムな (slim, from English).