Klimas attended law school at the University of Moscow. After graduating, he returned to Vilnius and served on the Lithuanian Central Relief Committee. He was elected to the Council of Lithuania in 1917, and signed the Act of Independence in 1918. Klimas went on to serve as the Lithuanian diplomatic envoy to France, Belgium, Spain, Portugal, and Luxembourg.
During the Interwar period Klimas published a number of scholarly works, including Russich Litauen, a study of Russian rule of Lithuania from 1795 - 1915; Der Werdegang des litauischen Staates, describing the emergence of the Lithuanian state from 1915 - 1918; and Lietuvos žemės valdymo istorija, a history of land ownership in Lithuania.
While he was serving on a diplomatic mission to Paris in 1940, the Lithuanian Legation was turned over to the Soviet Union. The Nazi occupational authorities in France arrested him in 1942, and he was sent to a concentration camp until 1943. He was released for a short while and returned to Lithuania, but was re-arrested in 1944 during the second Soviet occupation of Lithuania. This time he was sent to a concentration camp in Siberia and spent ten years there. His health was permanently impaired until his death in 1969.