Ragan Djaich hit the main line-up of the Red Star just six months after his debut for the youth club. Jajić made his debut for the main team on May 6, 1963, when the Stars trainer Aleksandar Obradovich released him for the match against the club Buduchnost from Titograd, and at that time Djaich was only 16 full years old. That match was the only one for Djaich that season, but from the next season, in which Zvezda became the champion of Yugoslavia, he became a regular player of the base. In 1964, 18-year-old Djaich was taken to the summer Olympic team 1964 games in Tokyo. From August 6, 1966, Jaich was the team captain . Soon, Djaich became the leader of a new generation of players “Red Stars”, who won three championship titles in a row from 1968 to 1970 . In 1968, thanks to successful performances for the club, coach Rajko Mitic included Dragan into the national team for the European Championship in 1968, the Yugoslav national team took second place at that championship, and Dragan himself thanks to two goals became the top scorer of the tournament. At the end of 1968, Jaich took third place in the dispute over the Golden Ball, losing only to two representatives of Manchester United, George Best and Bobby Charlton. In 1969, Jaich was named athlete of the year in Yugoslavia, and was again nominated for the Golden Ball. In the 1970/71 season, Djaich, together with the Red Star, made it to the European Champions' Cup semi-finals, where he lost to Panathinaikos in Greece only in the sum of two matches. Between 1971 and 1975, except for 1974, Djaich was constantly nominated for the Golden Ball.