She graduated from the Tallinn University of Technology and worked as an architect in the organs of the State Planning Commission, then as a technician and technologist in design institute in Tartu.

On 10 October 1981, Parek participated in the signing of an open letter to the heads of government of the USSR and the countries of northern Europe, in which the authors (38 Lithuanians, Latvians and Estonians) supporting the Soviet leadership, approved the Scandinavian Nuclear-weapon-free zone initiative and proposed to extend this initiative to the Baltic states, as well as proposing the removal of Soviet missiles from their territory.

On 5 March 1983, Parek was arrested and on 16 December sentenced by the Supreme Court under Article 68 Part 1 of the Criminal Code of the ESSR (corresponds to Art.

Other defendants in the same case, charged with the same crimes, were Heiki Ahonen (who later became the director of the Museum of Occupations in Tallinn) and Arvo Pesti (both born 1956).

For a time she served in Dubravlag labor camp in the so-called "small area" for women who have been convicted of political crimes.

Along with Tatyana Velikanova, Irina Ratushinskaya and others, Parek took part in the hunger strikes and other protests, for which she was subjected to imprisonment in solitary confinement.

Parek participated in the presidential elections in Estonia on 20 October 1992, taking fourth place with 4.3% of the vote.