Video report by ITV News Royal Editor Chris Ship
The 39-second clip, posted on their official Twitter account, shows the family at their Norfolk residence, Anmer Hall, and on sand dunes at a nearby beach.
It comes as the couple celebrate 10 years of marriage.
Watch a new video released by the Cambridges of the family in Norfolk in Autumn last year
Earlier, they had released two new pictures to mark their 10th wedding anniversary.
The photographs, published on Wednesday night, show Kate and William embracing in the grounds of Kensington Palace. They will celebrate the milestone on Thursday.
The pair married at Westminster Abbey after an eight-year relationship.
The pair were flatmates at the University of St Andrews.
Kate has now spent a decade as a fully signed up member of the royal family, an HRH, a duchess and a future queen, with the pair marking their milestone as husband and wife on Thursday.Ten years on, the couple have three children, seven-year-old Prince George, Princess Charlotte, five, and three-year-old Prince Louis.
Kate has focused her charity work on early years, young people’s mental health, the visual arts and promoting the benefits of outdoor life.
The Royal Family wished the couple well via social media.
And William's father, Prince Charles together with Camilla, also congratulated the couple on their 10 years together.
During the Covid-19 crisis, the Cambridges have been supporting key workers and frontline NHS staff with video calls and face to face engagements when permitted, and promoting the vaccine drive.
They also became joint patrons of NHS Charities Together.
The 240 NHS charities in the UK provide extra funding and additional services above and beyond what the NHS core-funds, supporting hospitals, community and mental health services, and ambulance services.
Watch ITV News report on William and Kate’s wedding from 2011
The traditional gift on a 10th wedding anniversary is tin, symbolising strength and durability.
The Cambridges have faced personal challenges over the past year, dealing with the fallout from Megxit and the Sussexes’ bombshell Oprah interview.
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The Sussexes plunged the monarchy into crisis just weeks ago when they accused the royal family of racism and the institution of failing to support Meghan when she was suicidal.
Kate was publicly singled out by Meghan in the primetime television show as having made her cry in the run-up to her wedding.
It was a disagreement over flower girl dresses and Meghan said the Palace failed to correct reports which said she left Kate in tears.
Kate has been suggested as a potential peacemaker who might be able to heal the ongoing rift between William and his brother the Duke of Sussex.
Harry appeared to smile briefly at his sister-in-law as the three talked together after the Duke of Edinburgh’s funeral, with Kate then stepping back which allowed the brothers to continue walking with one another.
Last Friday was yet another big day for the Cambridges - their son, Prince Louis, turned three. To mark his birthday, the Duke and Duchess released a photo of the young royal on his first day of nursery school.
Louis has followed in the footsteps of big sister Princess Charlotte, aged five, who also attended the same nursery.