His first major client was Dallas, Texas hotel owner Ben Whitaker for whom "Jimmy" Conway conditioned the 1948 and 1953 American Champion Three-Year-Old Filly, Miss Request and Grecian Queen.
Owned by Ada L. Rice, Pucker Up was the 1957 American Champion Older Female Horse.
From 1962 to 1966 Jimmy Conway trained for John Galbreath's Darby Dan Farm with whom he would enjoy his greatest success.
Following a lengthy illness, Jimmy Conway died at age seventy-three at Nassau Hospital in Mineola on Long Island, New York.
In 1996 he was inducted in the United States' National Museum of Racing and Hall of Fame.