Complex sentence: Her film roles began with "Up the Down Staircase" starring Sandy Dennis in 1967, and in 1973 was called by Mike Nichols to play a small role in his film "Day of the Dolphin".
Split into simpler sentences: Her film roles began with "Up the Down Staircase" (which starred Sandy Dennis) in 1967. In 1973 she was asked by Mike Nichols to play a small role in his film "Day of the Dolphin".