Wright became a member of the Houston Symphony after graduating and in the following year became principal clarinetist of the Dallas Symphony. He went on to become the principal clarinetist of the National Symphony in Washington D.C. and played there until joining the Boston Symphony Orchestra in the 1970–1971 season.
Wright's professional journey began after he graduated, as a member of the Houston Symphony. The following year, he became the lead clarinetist of the Dallas Symphony and later held the same position with the National Symphony in Washington D.C., before joining the Boston Symphony Orchestra during the 1970-71 season.