Depkat won the first prize for cello at the 1964 Geneva International Competition. In 1966, she became a diploma winner at the Tchaikovsky Competition in Moscow. On December 7, 1966, she was named the second-prize winner of a Concert Artists Guild Competition in recital at The Town Hall in New York. Depkat went on to receive first prize at the Boston National Instrumentalist Competition in 1967, and was later appointed the American representative of Jeunesses Musicales at Expo 67 in Montreal for whom she went on tour in European countries such as Belgium, Denmark, France, Italy and the Netherlands as well as the United States. She joined the faculty of the University of Texas at Austin in late 1967. Depkat won first prize at the 10th CBC Talent Festival and was named a diploma winner at Casals Competition in Budapest the year after. She was selected by the Boston-based Group W station WBZ-TV as the United States' outstanding young instrumentalist in July 1967, earning a scholarship to New England Conservatory of Music.