Complex sentence: Parthasarathy was a "Sangeetha Bhushanam" of Annamalai University at a time when veterans like Ponniah Pillai (of the Thanjavur quartet family) and violinist and Sangita Kalanidhi T.S. Sabesa Iyer taught there.
Split into simpler sentences: Parthasarathy was a "Sangeetha Bhushanam" of Annamalai University. During his period at this university veterans like Ponniah Pillai (of the Thanjavur quartet family) and violinist and Sangeetha Kalanidhi T.S. Sabesa Iyer taught there.