He was a tachiyaku actor (performer of male roles), specializing in playing the roles of young, handsome lovers in the wagoto style, a type of role known as nimaime. Kan'ya is also known for his early postwar film career, and as the adoptive father of Bandō Tamasaburō V, the most famous and popular onnagata (specialist in female roles) of today. Kan'ya was the fourteenth in the line of actors and theatre managers to hold the name Morita Kan'ya.
Previous bearers of the name were managers (zamoto) of the Morita-za kabuki theatre in Edo (later Tokyo) until 1894. Kan'ya was adopted by Morita Kan'ya XIII, and in turn was the adoptive father of Bandō Tamasaburō V.
Kan'ya made his first appearance onstage at the age of seven, at the Kabuki-za in Tokyo, under the stagename Bandō Tamasaburō IV. In the early postwar years, Kan'ya acted in a number of films, including Surōnin Makaritōru (1947), Otomi to Yosaburō (1950), and Edo no Hanamichi (1953). Remaining quite active on the kabuki stage as well, Kan'ya performed in many revivals at the National Theatre, taking part as well in the Theatre's 1966 opening ceremonies and the associated performance of Sugawara Denju Tenarai Kagami.
Kan'ya made his last Tokyo stage appearance in December 1974, in a production of Kanadehon Chūshingura at the National Theatre, and his final stage appearance the following month, at Nagoya's Chunichi Theatre. He died on 28 March 1975.