Kārlis Klāsups participated in the Latvian Chess Championship finals 12 times.

(1950,[2] 1955[3]) but in 1959, Kārlis Klāsups reached the greatest success in own career and divided first place in this tournament with Pēteris Kampenuss.

Kārlis Klāsups won additional match for Latvian title - 4:3.

[4] He has participated in USSR Chess Championship preliminary tournaments in 1955[5] and 1959[6] but without great success.

Also, Kārlis Klāsups played for Latvia in 1955, at sixth board in 4th Soviet Team Chess Championship in Voroshilovgrad and won the third place (+2 −1 =6).