Emergency services attended and she was pronounced dead at the scene.
Police Scotland had been attempting to trace the driver of the vehicle which officers said failed to stop at the scene.
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On Saturday, the force announced it had arrested a man, who was later released pending further inquiries.
Detective Inspector Jan MacColl said on Friday: “Our thoughts are with Elizabeth’s family, friends and everyone affected by this tragic incident. Officers will continue to support her family as our inquiries progress.
“I would urge anyone who witnessed the crash, or who may have seen a white car in the area around that time, possibly with damage, to come forward.
“We would also ask anyone with dashcam footage that could assist our investigation to please get in touch.
“Anyone who can help is asked to call 101, quoting incident number 2566 of December 31.”