Kjær was born in Ullits on 9 January 1893. In 1915 he received a teaching diploma and worked as a teacher and then a librarian in Brønderslev until 1935 when he was elected to the Parliament. He served there until 1943. He was appointed minister of interior to the cabinet led by Prime Minister Knud Kristensen in 1945. He was one of the right-wing members of the cabinet. He supported the suggestions to improve the treatment of mental illness using new psychiatric approaches and techniques. Kjær died at a hospital in Copenhagen on 18 June 1947 while serving in the post and was buried in Brønderslev.
