The incident took place around a mile north of the Granthouse junction with the A6112 at around 11.50pm on Thursday.
Emergency services attended the scene and a 50-year-old woman was pronounced dead at the scene.
Police said there were no reports of other injuries.
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The road was closed while investigations were carried out, and re-opened at around 8.30am on Friday.
Sergeant Dave Waddell said: “Our thoughts are with the family and friends of the woman who died at this difficult time.
“Our enquiries are ongoing to establish the full circumstances and I am appealing for anyone who witnessed the crash and hasn’t already spoken to officers to get in touch.
“I would also appeal to anyone who was in the area and may have dash cam footage which could assist to contact us.”
Anyone with any information is asked to contact 101 quoting reference 4019 of August 28.