From 1952 to 1967, McConkie was an instructor in business law at
Stevens–Henager College. He was the county attorney for
Summit County, Utah from 1959 to 1963. Like his father, McConkie became a prominent Utah
Democrat, and in 1960, he was the Utah
point man for the
John F. Kennedy 1960 presidential campaign. From 1955 to 1957, McConkie was a member of the
Utah House of Representatives. McConkie was elected president of the Utah State Senate during his first term in office. It was the first time a state senator in his initial term was elected president of the senate since the beginning term of the Utah State Senate. In 1956, he ran against
William A. Dawson for
Utah's 2nd congressional district. He also served very briefly in 1965 and in 1966 as acting governor when both the governor and secretary of state of Utah were not in the state. McConkie was president of the
Salt Lake City School Board McConkie argued the case that led to a broadening of the
clergy-penitent privilege in Utah to include any information that was given by a parishioner to a cleric with the intent of getting spiritual advice. McConkie has been involved in international law, having drafted laws that were enacted in both
Jamaica and
Mauritius. McConkie was a key figure in the process of getting official recognition of the LDS Church in
Zaire in 1986. McConkie was named lawyer of the year by the
Utah State Bar in 2007. ==Personal life==