She was born on 10 March 1924 under the name of Walter "Wally" Stott.
According to her friend and colleague Max Geldray, she struggled with her gender identity throughout her life, and according to her wife, Christine Parker, Morley probably tried hormone replacement therapy at some point before they met.
Morley won three Emmy Awards for her work in music arrangement. These were in the category of Outstanding Music Direction, in 1985, 1988 and 1990, for Christmas in Washington and two television specials starring Julie Andrews.
Morley was a transgender woman and began transitioning to live openly as a woman in 1970, at the age of 46.
Morley underwent sex reassignment surgery in Casablanca in June 1970 and publicly came out as a woman in 1972. She chose the new surname Morley as it was her grandmother's maiden name.