Principally a trainer, Veitch has an accomplished resume, which also includes work in consulting and broadcasting. He has been nominated as a trainer to the National Museum Racing Hall of Fame for the past three years and was inducted into Bradley University's (his alma mater) Sports Hall of Fame in the late 1980s. Veitch trained for Lexington's legendary Calumet Farm from 1976 to 1983 and surfaced on the 1978 Triple Crown trail with Alydar, who finished second to Affirmed in all three races. Veitch went on to train for the Galbreath's Darby Dan Farm from 1984 until the late 1990s, a stint that included 1985 Breeders' Cup Classic winner, Proud Truth, and 1988 champion grass horse, Sunshine Forever.In 1999 Veitch took a one-year contract with Prince Faisal bin Khalid in Saudi Arabia. After his return to the states he worked half a year for Calumet's Henryk de Kwiatkowski, who purchased the bankrupted farm in the early 1990s with hopes of revitalization. Veitch went on to work two years for John Ed Anthony before the KHRA approached him last fall about a possible state steward position.
Veitch also worked as a color commentator on NBC's Breeders' Cup program from 1990 to 1998, and ABC's Triple Crown coverage in 1982 and 1983.