[1][2] Kiær studied zoology and then paleontology for three years under Professor Karl Alfred von Zittel (1839–1904) at Ludwig Maximilian University of Munich where in 1896 he received his doctorate.
In 1909 he was appointed professor of paleontology at the University of Oslo, as the first in Norway to hold such a position.
[3][4] His most important publication was his doctoral dissertation from 1906, Das Obersilur im Kristianiagebiete.
[4][5] Kiær was responsible for the construction of the paleontological section of the Paleontologisk Museum at Tøyen in Oslo.
He was an important inspiration for the work of palaeontologist Anatol Heintz (1898–1975) who was director of the Paleontological Museum from 1940.