[5] At the 2020 European Boxing Olympic Qualification Tournament in London, which was interrupted due to the COVID-19 pandemic and continued in Paris in 2021, Terteryan won the opening round against the Kosovar Shpëtim Bajoku, but lost in the round of 16 to the Belarusian Dzmitry Asanau.

[8] In 2022, Terteryan won the gold medal in the welterweight division at the U22 European Championships in Poreč, defeating Oliwier Zamojski from Poland, Chris-Marco Eloundou from Germany, Yaroslav Mykhalushko from Ukraine, Nabi Iskandarov from Azerbaijan and Ioan Croft from Wales.

[11] In 2023, Terteryan also won the European Games in Kraków in the light middleweight category, defeating the Portuguese Diogo Marcelino, the Italian Salvatore Cavallaro, the Albanian Alban Beqiri, the Turk Tuğrulhan Erdemir and in the final against the Serbian Vahid Abasov.

[13][14] At the 2024 Olympics in Paris Terteryan reached the quarterfinals after a win against Makan Traoré in the round of 16.

After Tigran participated in the super heavyweight division at the 1996 European Championships in Vejle, Denmark, he stayed in the country and applied for asylum in order to avoid conscription in Armenia.