She later sang with the Beecham Opera Company in roles such as Nedda, Santuzza, Musetta, Elsa, Desdemona, Sophie, and the Countess in The Marriage of Figaro. In 1915 she was the soprano soloist in Sir Edward Elgar's incidental music for the first production of Algernon Blackwood's The Starlight Express. During the development of the production, she and the other soloists were regular visitors at Elgar's home. In 1914 she married John Mundy, a free-lance cellist who worked with the London Symphony Orchestra, Albert Hall Orchestra, Beecham Opera Company and elsewhere. They had two children in London: a daughter, Margaret "Meg" Mundy, later an actress and singer, and a son, , later a renowned medievalist and Professor Emeritus of History at Columbia University. In 1921 they left for the United States with their children, settling in New York, and becoming well known for their joint recitals featuring early English music. She also sang in opera in America and beyond while contracted to , and her husband became principal cellist and orchestra manager for the Metropolitan Opera. He also collaborated with Edward Eager on composing a musical comedy, The Burglar's Opera, which was also staged under other titles, such as The Liar, The Burglar, The Rascal and The Gay Rascal. Clytie Mundy retired from performing in the late 1920s, and became a renowned singing teacher. She maintained a private class of twenty-five vocal students, a choral class of about twenty, two vocal quartet parties, and a women's trio. Her notable students included Marge Champion, Alfred Drake, Nanette Fabray, Kathleen Ferrier, Celeste Holm, Peter Pears and David Wayne. Peter Pears had been studying singing under Therese Behr, but transferred to Mundy in 1940. He had almost daily lessons with her, and his partner Benjamin Britten would often also attend, as accompanist. Pears found her "a wonderful woman to work with, very sympathetic and forthright". She became lifelong friends with Pears and Britten. To help secure an American premiere of Britten's opera Peter Grimes in 1946, she hosted three private performances of excerpts at her apartment for Serge Koussevitzky, Leonard Bernstein, Ralph Hawkes and others. Pears returned to her for some more lessons in 1948. Britten dedicated his setting of the song "Down by the Salley Gardens" to Clytie Mundy, and his setting of the Scottish lullaby "O can ye sew cushions?" to her daughter Meg. They also named their pet miniature dachsund "Clytie" after her.
