Her best-known role was as "Resi Berghammer" in the German television series, Der Bulle von Tölz, in which she played the mother of the eponymous cop.

Born in Vilshofen an der Donau, near Passau, Drexel trained as an actress in Munich, where she was also given her first engagement.

She also appeared, to great critical acclaim, in new plays by Franz Xaver Kroetz and Felix Mitterer.

Drexel's early television work included Wedekind's Der Marquis von Keith (1962), a German adaptation of Shaw's Candida (1963), Frisch's Biedermann und die Brandstifter (1967), and Kroetz's Wildwechsel [de] (Jail Bait), directed by Rainer Werner Fassbinder (1972).

Drexel was a member of the cast of the cult television series Münchner Geschichten [de] (1974) and Zur Freiheit (1987).