From 1967 to 1969 Arrate studied in the U.S. and from 1973 to 1987 he lived in exile in Rome, East Berlin and Rotterdam.
In 2013, Quintana won stage 3 of the Volta a Catalunya, and the following month, he won the queen stage of the Tour of the Basque Country by sprinting to victory after the final climb in Eibar–Arrate, two seconds before a group of six fellow overall contenders.