Born as Clarence Kivovitch to Morris Kivovitch and Anna Katz, Clarence Kivett began attending the University of Kansas (KU) in 1924 and graduated with a bachelor of science degree in Architecture in 1928. Later that same year, Kivett started his career as an architect at the Madorie and Bihr architectural firm in Kansas City.

In 1929, Kivett left Madorie and Bihr to work for Hoit, Price, and Barnes, one of the largest architecture firms in the Kansas City area at the time. However, due to a slow down of construction work during the Depression, Kivett was laid off and began his own architectural design office. With his new office, Kivett's first big commission was designing the Katz Drugstore at Main and Westport Road with the Bloomgarten and Frohwerk architectural firm for his uncles Ike and Mike Katz. Kivett incorporated what would later be coined as an Art Deco design for the store, inspired in part by a building Kivett saw at the 1933 Chicago World's Fair. The store opened in December 1934. Kivett married Margaret (Heimovics) Kivett, who he met while studying at KU, later that same month. In 1935, Kivett changed his surname from Kivovitch to Kivett.

In 1940, Ralph Myers joined Kivett at his architectural design office, and after World War II, became a partner for the new firm Kivett and Myers, Architects and Planners. From 1945 to 1975, Kivett and Myers became one of the most prominent mid-century architectural firms in Kansas City, responsible for the design of several major landmarks and buildings in the area, including the Spencer Chemistry and Biological Sciences Building at the University of Missouri-Kansas City (completed in 1968), the Temple B'nai Jehudah at 69th and Holmes (completed in 1969, now demolished), and the Alameda Plaza Hotel (completed in 1972 and now the InterContinental). Kivett and Myers also gained national attention for its 1967 design of the Truman Sports Complex and 1972 design of the terminals and control tower at the Kansas City International Airport.

With being credited as bringing modern architectural design to Kansas City, Kivett and Myers are also often credited as fostering a generation of modernists and serving as an important training ground for many leading architects. Kivett and Myers received over 200 design awards, including winning 30 of the 73 design awards given by the local chapter of the American Institute of Architects (AIA) from 1945 to 1975, with another 40 of the 46 AIA chapter awards given from 1975 to 1993 being awarded to architects mentored under Kivett and Myers.

In 1975, Kivett retired, and Kivett and Myers was merged with HNTB Architects. Clarence Kivett passed away in 1996 at the age of 91.