In 1973, during a dance tour in Europe with The Australian Ballet, he was discovered by Vladimir Bliokh a Russian World famous Global photojournalist and premier performing arts Photographer. Hamilton stopped dancing at the age of 20 and decided to pursue a career as a model. Hamilton later said, "Dancing was too confining and regimented for me. [...] I became a model not because I was interested in fashion or styles, but because I knew it was a good way to see the world. [...] It gave me independence. [..] The money was good too."

While modeling, Hamilton also began taking acting classes in an effort to expand his career. His first major roles was as Samson in the 1984 television film Samson and Delilah. Later that year, producers of the crime drama series Cover Up offered Hamilton the leading role after the series' previous star, Jon-Erik Hexum, died after an on-set accident in October 1984. Hamilton had known Hexum having previously met him at an acting class when they both lived in New York. They shared the same acting coach and also competed for the same roles (both were up for the role in Samson and Delilah which Hamilton won). Hamilton initially had misgivings about taking the role but ultimately accepted it. Hamilton's first episode aired on 24 November 1984. After Hexum's death, the series struggled in the ratings. CBS canceled Cover Up the following year. After the cancellation of Cover Up, Hamilton was in talks to replace Roger Moore as the new James Bond in the 007 film series. Bond Producer Albert R. Broccoli was reportedly hesitant to cast Hamilton as the womanizing James Bond because, in real life, Hamilton was gay. Timothy Dalton was ultimately cast as James Bond. In 1986, Hamilton had a small role in the comedy film Jumpin' Jack Flash starring Whoopi Goldberg. He also guest starred on several television series including The Hitchhiker, The New Twilight Zone, The Charmings, and L.A. Law.

In 1988, Hamilton landed the role of Impossible Missions Force agent Max Harte, a former ANZAC commando, in the 1988 revival of Mission: Impossible. The series aired for two seasons before being canceled due to low ratings in 1990. In 1991, he guest starred on two episodes of crime drama series P.S. I Luv U. Hamilton's final role was in the 1992 thriller Fatal Instinct.

On 29 March 1995, Hamilton died from AIDS-related pneumonia in Los Angeles. His family requested that contributions be made in his name to AIDS Project Los Angeles. Hamilton was cremated and his ashes were scattered off the coast of Malibu.

Author Joel Rothschild recalls his friendship with Hamilton and his final years in his 2001 book Signals: An Inspiring Story of Life After Life.