He was the son of Christen Christensen Elster (1804–1891) and Elen Sophie Alstrup (1811–1889).
In 1867, he traveled to Germany to receive training as a forester at Giessen.
From 1873, he was employed as a forester first in Valdres and then in Trondheim where he resided until he died of pneumonia in 1881 at age 40.
[2] He was married in 1874 to Sanna Fasting (1845–1926) and was the father of Kristian Elster the Younger (1881-1947).
He made his literary début with the historical drama Eystein Meyla, which was staged in 1863.