In 1961, he played the roles of John Keller in "We're Holding Your Son" on the anthology series hosted by Ronald W. Reagan, General Electric Theater, and Ernie Taggart in "Voyage into Fear" of the CBS detective series, Checkmate. In 1962, Brady was cast in the lead guest role as reporter/commentator Floyd Gibbons in "The Floyd Gibbons Story" of ABC's The Untouchables, starring Robert Stack. The next year he portrayed Bill Floyd in the episode "Run for Doom" of CBS's The Alfred Hitchcock Hour. In 1967, Brady guest starred on Carl Betz's ABC legal drama, Judd, for the Defense. In 1969, he portrayed Budd Blake in the episode "Panic" of the NBC drama Bracken's World. In 1973, he was cast as Davey Collier in "No Stone Unturned" of NBC's Banacek. From 1975 to 1977, Brady had the recurring role of "Vinnie" in sixteen episodes of NBC's Police Story crime drama.