He won the silver medal at the 1992 World Junior Championships, held in late 1991 in Hull, Canada.
He first competed for Latvia in January 1992, placing 9th at the European Championships in Lausanne, Switzerland.
Kostin's highest continental placement was 4th, which he achieved at the 1993 European Championships in Helsinki, Finland.
Kostin finished 8th at his sole Grand Prix event, the 2000 Trophée Lalique.
Kostin has served as the director of skating at the Yarmouth Ice Club in Kingston, Massachusetts,[2] and an international technical specialist for Latvia.