Both of her parents were communist activists who had been incarcerated by Estonian authorities in the early 1920s during the Trial of the 149 for their political activity and released in 1938, the year prior to her birth.

Following the German occupation of Estonia during World War II in July 1941, she was evacuated to Samara Oblast in the Ural Mountains of Russia with her mother and grandmother.

Among her classmates were noted future actors Tõnu Aav, Mikk Mikiver, Maila Rästas, Aarne Üksküla, Madis Ojamaa, Jaan Saul, Meeli Sööt, and Mati Klooren.

[7] After graduating from the Tallinn State Conservatory, Ines Parker began a two-year engagement as a stage actress at the Ugala theatre in Viljandi in 1961.

[8][9] During her engagement at the Philharmonic, former Tallinn State Conservatory classmate Madis Ojamaa developed a comedic, satirical character called Eliisabet Jõhvi for Parker.

[10] As Ines Parker, she began her film career with a small role in the 1960 Herbert Rappaport-directed drama Vihmas ja päikeses for Tallinna Kinostuudio (now, Tallinnfilm).

This was followed by the more significant role of Laine Arro in the 1962 Igor Yeltsov-directed drama Ühe katuse all, based on the 1957 novel Ühes majas by Estonian author Hans Leberecht.

The following year she appeared in the Arvo Kruusement-directed drama Karge meri, based on the 1938 novel of the same name by author August Gailit, which chronicles the difficult lives of traditional Estonian seal hunters on the Baltic Sea coast.