Stapley was born in Westcliff-on-Sea, Essex, England, in 1923. A writer, Stapley published his first novel when he was just 17 years old. He served in the Royal Air Force during World War II.

Following the end of War War II, Stapley began appearing in theater roles in London. He soon signed with Metro-Goldwyn-Mayer (MGM), making his film debut in the 1948 movie, The Three Musketeers, opposite Elizabeth Taylor. He next appeared in the 1949 remake, Little Women, in which he played John Brooke, the love interest of Janet Leigh's character, Meg.

He continued to appear in a string of Hollywood films at different studios during the 1940s and 1950s, including the 1951 horror film The Strange Door, which co-starred Boris Karlof;1953's King of the Khyber Rifles, opposite Tyrone Power; Charge of the Lancers with Paulette Goddard; and The Iron Glove with Robert Stack in 1954.

Stapley returned to the United Kingdom and Europe in 1960, where he adopted the stage name, Richard Wyler. His British television credits from that era included the crime series, Man From Interpol. He also appeared in a series of European-made adventure and western films using the name, Richard Wyler, including The Barbarians, The Rattler Kid, The Bounty Killer, Dick Smart, and The Girl From Rio, which co-starred Shirley Eaton and George Sanders.

During the 1970s, Stapley returned to film roles under his birthname, Richard Stapley. He co-starred in the 1970 film, Connecting Rooms, opposite Michael Redgrave and Bette Davis. He was also cast in Alfred Hitchcock's Frenzy.

Stapley became a naturalized U.S. citizen during his later life. He focused on writing following his acting career. He published a novel entitled, Naked Legacy, in 2004. Stapley also completed a second novel and corresponding adapted screenplay, both called Tomorrow Will Be Cancelled. He was working on an autobiography at the time of his death in 2010.

Richard Stapley died of kidney failure at Desert Regional Medical Center in Palm Springs, California, on March 5, 2010, at the age of 86. His death was announced by his publicist, Alan Eichler.