Friedemann played several times in Estonian championships at Tallinn. In 1935, he lost a match against Keres at Tallinn (+1 –2 =0). Friedemann played for Estonia in Chess Olympiads:
In 1935, on second board in the 6th Chess Olympiad in Warsaw (+6 –6 =7);
In 1936, on third board in 3rd unofficial Olympiad in Munich (+9 –5 =6);
In 1937, on reserve board in the 7th Chess Olympiad in Stockholm (+6 –2 =5);
In 1939, on fourth board in the 8th Chess Olympiad in Buenos Aires (+11 –3 =3).
Keres (1st board) and Friedemann (4th board) contributed mostly to the success.
During World World War II, he twice played against Keres in team matches in 1940. He died at the age of 34.
Gunnar Friedemann vs Paul Keres, Tallinn 1935, match, Queen"s Gambit Declined, D52, 1-0
Gunnar Friedemann vs Chris De Ronde, Buenos Aires 1939, 8th Olympiad, Neo-Grünfeld, D78, 1-0
Paul Keres vs Gunnar Friedemann, Tallinn 1940, Queen"s Indian, E17, ½–½.