Alice Kertész took up gymnastics in 1949 and won her first medals at the Hungarian national championships in 1954, placing second in the uneven bars and the balance beam, and third in the horse vault. She also attended the World Championships that year, bringing home silver in the team all-around and winning the team portable apparatus competition. The following year she captured her first national title with gold in the team all-around, also taking silver in the balance beam, and bronze in the uneven bars and individual all-around. After taking silver in the uneven bars and the horse vault in 1956, she was selected to represent her country at the Melbourne Olympics, where she won gold and silver in the portable apparatus and all-around team events respectively. Her best individual finish was joint-sixth (with compatriot Olga Tass-Lemhényi) in the uneven bars.
Kertész won two more national titles, in the uneven bars and the balance beam, in 1958, but retired in 1960 before the Rome Olympics. That same year she graduated from the College of Physical Education and eventually worked as a teacher and coach at both the club and university level. She also had a brief tenure as head of the women’s national team in the early 1980s.