During his sporting career, Yury Starunsky played with two clubs – until 1970 with SKA Kyiv and from 1970-82 with CSKA Moskva. With CSKA Moskva, Starunsky won 13 Soviet titles in a row (1970-82) and won the European Champions League five times (1973-75, 1977, 1982). Internationally, Starunsky played with the Soviet national team from 1970-76, winning Olympic silver (1976) and bronze (1972), silver at the 1974 World Championships, and was twice a European Champion (1971, 1975).
After finishing his sporting career Starunsky worked as a volleyball coach, coaching the Soviet national women’s team from 1983-87 and coaching CSKA Moskva women’s team from 1983-88. From 1988 until his death, he worked as a prorector of physical education at the Moscow Institute of Physical Culture. In the 1990s and 2000s he was also the head coach of the Spartak Moskva volleyball team.