。
She pioneered a new way of playing jazz on the shamisen.
Literal
She [topic-は] shamisen [by means of-による] new jazz [genitive-の] performance-method [object-を] started.
An unusual cultural pairing. 三味線 (shamisen) is the iconic three-stringed Japanese instrument played with a plectrum (撥, バチ), traditionally used in 歌舞伎, 浄瑠璃, and folk music. ジャズ is the standard katakana loanword for jazz. The による is the prenominal form of によって ('by means of, using'), here marking the shamisen as the instrument. 演奏法 ('method of performance') stitches 演奏 ('musical performance') + 法 ('method, way'), the productive ~法 suffix used to label techniques. Modern shamisen players have indeed experimented with jazz, rock, and other Western genres — a notable strain of contemporary fusion music.