He also participated in conducting master classes with Franco Ferrara, Sergiu Celibidache, and Arvīds Jansons.
After winning the Karl Böhm conductor's competition in 1979, he made his debut at the Vienna State Opera in 1981 with Stravinsky's Petrouchka.
From 1984 to 1994, Graf was music director of the Mozarteum Orchestra of Salzburg, where he recorded the complete symphonies and other works by Mozart.
In 2018, he won a Grammy award for his recording of Alban Berg's Wozzeck with Anne Schwanewilms, Roman Trekel and the Houston Symphony.
In July 2019, the Singapore Symphony Orchestra announced his appointment as its new chief conductor, effective with the 2020-2021 season.