stage career; life on the stage
Refers to a person's career or life spent performing in theater, dance, or similar stage arts.
She has been living a stage life since she was young.
Over a long stage career, he has played many roles.
芸能生活 is broader, covering entertainment careers in general (TV, film, music), while 舞台生活 specifically refers to stage performance.
Compound of 舞台 (stage) and 生活 (life, living). The meaning is transparent from its components.