During the 1950s and 1960s, she made numerous guest appearances on a variety of television programs, including the critically acclaimed science fiction anthology series The Twilight Zone, which premiered in 1959, as well as the popular medical drama Dr. Kildare, which aired from 1961 to 1966. Additionally, she appeared on the crime drama The Felony Squad, which debuted in 1966, the long-running western series Gunsmoke, which first aired in 1955, the historical drama Daniel Boone, which premiered in 1964, and the detective series Mannix, which aired from 1967 to 1975.
She also had a short role as Doris Schuster on the popular prime-time soap opera Peyton Place, which aired from 1964 to 1969. Furthermore, she appeared on the daytime drama Bright Promise, playing the recurring character Ann Boyd Jones from 1969 to 1972.
As her acting career progressed, Kobe began to transition behind the camera, taking on roles as supervising producer and associate producer on several daytime programs, including the soap opera The Edge of Night, which premiered in 1956, and its spin-off series Return to Peyton Place, which aired in 1972. In 1982, she became the executive producer of the prime-time drama Texas, which was in its final few months of production.
Kobe then went on to become the executive producer of the iconic soap opera Guiding Light, which debuted in 1952, a position she held from 1982 to 1987.