Kavalírová was born Naděžda Morávková in Opočno, Czechoslovakia, in 1923. In 1948, following the takeover of Czechoslovakia by the Communist government, Kavalírová was expelled from the faculty of the School of Medicine at the Charles University in Prague due to her membership in the Czech National Social Party. She soon became actively involved in the country's opposition movement against the Communist government. In 1956, Kavalírová was convicted of treason and espionage against the Communist government. She was sentenced to three years as a political prisoner from 1956 to 1959. She was a member of Czechoslovak National Socialist Party and participated in a student march to Prague Castle.