From the end of the 1940s to the start of the 1960s, she was one of England's leading women chess players. Eileen Betsy Tranmer four times won the British Women's Chess Championships: 1947, 1949, 1953 and 1961. In 1950, Eileen Betsy Tranmer participated at Women's World Chess Championship in Moscow where shared 5th-7th place. In 1952, she participated at Women's World Chess Championship Candidates Tournament in Moscow and ranked 7th place. In 1950, she was awarded the FIDE International Women Master (WIM) title.