In the 2012–13 season, Gosviani was the third alternate for a place at the senior Russian Championships and was admitted after three skaters withdrew. She finished sixth in her debut at the event. With several skaters above her not age-eligible, Gosviani was named to the Russian team for the European Championships. She attained the minimum TES for the event at the Toruń Cup, where she won gold in the junior ladies' event. Gosviani made her senior international debut at the 2013 European Championships. She was twelfth in the short, fifth in the free, and sixth overall.