Teterev has represented Belarus in various international tournaments. He has played in the Chess Olympiads six times between 1992 and 2006, and he also played in the European Team Chess Championships in 2007, 2011 and 2013. He was also a member of the Belarusian team in the World Team Chess Championship of 2011.
In the individual tournaments, Teterev has a good track record. He has participated in the World Cup twice: in 2005 and 2007. He also finished 2nd in the Lithuanian Open Championship in 1996, tied for first in the Belarusian Championship in 1997, won the St. Petersburg Open in 1999, won the Vladivostok Open in 2009, and finished shared first in the Almaty Open in 2011.
Teterev has a education in law but he did not work in this field. Instead, he worked as a chess trainer from 2002.