Gibney was born September 11, 1961, in Manhattan Beach, California. She moved to Webster, New York, at a young age, returned to California to live several times, returning to Webster in 2004. She graduated from Buffalo State College with a major in theater, and later earned a Master of Fine Arts degree from the Yale School of Drama.
Gibney appeared twice on Star Trek: The Next Generation, once as a holodeck facsimile of Dr. Leah Brahms in the episode "Booby Trap" and later, as the real Dr. Brahms herself in "Galaxy's Child". In both these episodes she was Geordi La Forge's love interest. She also appeared on Star Trek: Deep Space Nine, in the episodes "Homefront" and "Paradise Lost", as Erika Benteen. She was considered for the role of Captain Kathryn Janeway on Star Trek: Voyager, but did not get the role. She was later considered for the role of Seven of Nine and tested twice. She was also considered, but likewise rejected, for the role of the Borg Queen in the film Star Trek: First Contact.