He was the son of Pedro Parra Avello and Haydée Alderete Banda. In 1956, he married María Cristina Jerez Horta, sister of senator Alberto Jerez Horta. The couple had one daughter in 1962.
He completed his secondary studies at the Salesian College of Valdivia and then entered the Law School at the University of Chile, graduating as a lawyer in 1957.
He joined the Christian Democratic Party in his youth and became active in its leadership. In 1965 he was elected as a deputy for Santiago’s 7th Departmental District, 1st District, serving until 1969. He was a member of the Permanent Commission of Foreign Affairs, which he chaired. In 1969 he ran for the Senate representing Tarapacá and Antofagasta but was not elected.[1]
He led the "Tercerista" faction of the Christian Democrats, which eventually split from the party in 1971. Alongside other former Christian Democrats such as Luis Maira, Pedro Felipe Ramírez, Luis Eugenio Díaz, and Osvaldo Giannini, he co-founded the Christian Left, becoming its first Secretary General.[2][3] The party joined the governing Unidad Popular coalition.
After the military coup he went into exile, continuing clandestine work for the party.[4] He reunited with his family in Sweden in the late 1970s and carried out academic work at the University of Uppsala.
With the return of democracy, he stepped away from active politics and became a professor at the Universidad Academia de Humanismo Cristiano and later at the Universidad Bolivariana de Chile. In 2011, he participated in the formation of the Broad Left Movement (MAIZ).[5]