Esmark took his theological exam in 1825 and first began his ministry as chaplain at Eidanger in Tromsø, Troms, Norway.
He commonly sent interesting specimens to his father, Jens Esmark, who was a professor of mineralogy and geology at the Royal Frederick University.
Morten Thrane Esmark located the first specimens of thorite, from which the element thorium is derived, on the island of Løvøya near Porsgrunn.
His father forwarded the specimen to Swedish chemist Jöns Jacob Berzelius, who confirmed that it was a new mineral which contained a new element.
The personal mineral collection of Morten Thrane Esmark was later donated to the Tromsø University Museum.