Her allegations, which Andrew strenuously denies, were struck from United States civil court records in 2015 after a judge said they were "immaterial and impertinent".
In the clip she describes the period as a "really scary time" for her.
"He knows what happened, I know what happened, and there's only one of us telling the truth", Giuffre, who claims Epstein made her have sex with the prince three times, says in the teaser.
It states: "Given the recent conduct of Prince Andrew in regards to his friendship with the convicted sex offender Jeffrey Epstein, we the residents of Inverness feel that it is inappropriate that Prince Andrew is associated with our lovely city".
Sources told Britain's The Sun that there is talk behind closed doors that the Queen, who has cut down on her royal duties and appearances in recent years, can not continue forever and that she will "retire" in April 2021 when she turns 95.
Virginia Giuffre (formerly Roberts) holds a photo of herself at age 16, when she says Palm Beach multimillionaire Jeffrey Epstein began sexually abusing.
Andrew, 59, and Buckingham Palace have always strenuously denied the accusations against him.
BBC Panorama is due to broadcast an hour-long programme which features an interview with Virginia Giuffre on Monday, 2 December.
After 67 years on the throne and witnessing some of the biggest events of the last century, Queen Elizabeth II is reportedly getting ready to take her most significant step back since her reign began.
"At first the Scotland Yard told me they were going to forensically examine GM's [Ghislaine Maxwell's] house in London - next thing I hear, just like the FBI, they were not allowed to pursue the investigation". The allegation was made against a United States national, Jeffrey Epstein, and a British woman.
He said the decision was reviewed after Epstein's death and police decided not to change policy. It related to events outside of the United Kingdom and an allegation of trafficking to central London in March 2001.
It comes after the UK's Metropolitan Police Service said today it would not reopen an investigation into an "allegation of non-recent trafficking for sexual exploitation" it received from Ms Giuffre in 2015.
Andrew, Elizabeth's second son, stepped down from royal duties last week saying the controversy surrounding his "ill-judged" association with late USA financier Jeffrey Epstein had caused major disruption to the royal family's work.
We therefore concluded that the MPS [Metropolitan police service] was not the appropriate authority to conduct enquiries in these circumstances.
Epstein killed himself in prison while awaiting trial on charges of conspiracy and trafficking minors for sex.
Earlier this month Charles laid a wreath on her behalf at the Remembrance Sunday service and the Duchess of Cambridge has taken on a number of her patronages including the Royal Photographic Society.