Jackson founded the Juilliard String Ensemble and was its first conductor 1970-71. He was associate or assistant conductor with the American Symphony Orchestra (1970-71) where he worked with Leopold Stokowski; the Baltimore Symphony Orchestra (1971-73); and the Rochester Philharmonic Orchestra (1973-87). He was appointed music director of the Flint Symphony Orchestra (Flint, Michigan) in 1982, the first black music director of the Dayton Philharmonic Orchestra in 1987 , and principal conductor of The Royal Ballet, Covent Garden, in 1986, and became its music director 1987-90. He was the first black person and the first American to occupy a chief position with the company.
He has been a guest conductor with orchestras such as the New York Philharmonic, 1978; San Francisco Symphony, 1984; Detroit Symphony Orchestra, 1983 and 1985; Cleveland Orchestra, 1983-84, 1986-87, and 1989-92; Boston Pops, 1983 and 1990-92, Toronto Symphony Orchestra, 1984 and 1990; Orchestre de la Suisse Romande, 1985 and 1988; BBC Concert Orchestra, 1987; and the Berlin Symphony Orchestra, 1989-91. He has also conducted the Vienna Symphony (European debut, July 1973), Houston Symphony, Indianapolis Symphony, Grant Park Festival Orchestra, Calgary Philharmonic Orchestra and the Louisville Orchestra.
He has also guest conducted the Helsinki Philharmonic Orchestra, Malmo Symphony, Gaeveleborg Symphony, Czech Symphony Orchestra (at the opening of the Prague Autumn International Music Festival), Stockholm Symphonic Wind Orchestra, Prague Radio Symphony Orchestra, Royal Liverpool Philharmonic, RAI Orchestra, Youngstown Symphony Orchestra, and the National Symphony Orchestra in Washington, D.C.. He has also performed with the Dance Theatre of Harlem at the Spoleto Festival in Italy and at the Royal Opera House, London. He was also music director of the New York Youth Symphony.
In 1973, at Leonard Bernstein’s suggestion, he was named as artistic director of the Vienna Youth Music Festival. He was the first person of color to conduct the Cape Philharmonic Orchestra. He is a particular favorite in Australia, having been principal guest conductor of the Quee
nsland Orchestra in Brisbane for three years and of the Canberra Symphony Orchestra. He has also led the Sydney Symphony, West Australian Symphony, Tasmanian Symphony, Adelaide Symphony, and Melbourne Symphony orchestras. He is also Musician in Residence at the Memorial Church, Harvard University.