Tirkey made his debut for the national side in February 2001 at the Akbar el Yom Tournament in Cairo against Belgium. He was a member of Indian team that participated in the Athens Olympic in 2004, where India finished seventh. In club hockey, Tirkey played for Services.
He is most remembered for his goal that he scored between Pakistan's ace striker, Sohail Abbas's legs in the final minutes of 2003 Asia Cup final to give India the winning lead after both teams were locked at 2-2 (India eventually added a 4th goal in the last minute). The match won India its first gold in Asia Cups.
Another highlight of his was in the Muruguppa Gold Cup in Aug 2001, where he scored a golden goal to win final, and thereafter in December 2002 during the National Games in Hydrabad.