Hægstad edited the newspapersNamdals Tidende and Namdalsposten, and was a co-founder of Nordtrønderen. He was elected member of the Parliament of Norway in 1891 and 1897; also serving as deputyrepresentative during the terms 1889–1891 and 1895–1897. He was appointed professor at the University of Oslo from 1899 to 1920. Among his works are Gamalt trøndermaal from 1899, Hildinakvadet from 1900, and Gamalnorsk ordbok med nynorsk tyding from 1909. He was the first chairman of Norigs Maallag, from its foundation in 1906.