。
She's taking private piano lessons.
Literal
She [topic-は] piano [of-の] private-instruction [object-を] is-receiving.
個人教授 is a Sino-Japanese compound — 個人 ('individual, private') + 教授 ('teaching, instruction') — and reads as 'private tutoring,' a more formal register than ピアノのレッスン. The verb 受ける ('receive') is widely productive for receiving services, instruction, treatment, examinations, and shocks: レッスンを受ける ('take a lesson'), 治療を受ける ('receive treatment'), 試験を受ける ('take an exam'). The progressive ~ている here marks the ongoing arrangement of taking lessons, not a single class.