Never seen before video or audio interviews with Cliff Burton is very rare these days. An ultra-rare audio interview with late Metallica bassist Cliff Burton, conducted by Ken of Metal Fanzine on January 31, 1984 in Cortland, New York (after Metallica's show at the Riverboat in Rochester, New York) has been posted at YouTube. A photo of Ken and Cliff can be found here.
As you probably remember, Clifford Lee Burton (February 10, 1962 – September 27, 1986) was a bass guitarist, best known for his work with Metallica from 1982-86. During a 1986 tour in Sweden, at the age of 24, Burton was crushed to death when the band's tour bus lost control and overturned.