Prince Edward also spoke about his father’s death, describing it as “a bit of a shock.”
The Duke of York suspended his public appearances in 2019 after a disastrous BBC interview about his ties to convicted sex offender Jeffrey Epstein.
The Duke of Sussex is staying at Frogmore Cottage in the U.K.
"I will miss my Grandpa, but I know he would want us to get on with the job," the Duke of Cambridge said Monday.
Officials on the eastern Caribbean island are worried about those who have refused to evacuate as the La Soufriere volcano fires ash and hot gas.
The country is considering mixing vaccines to help boost their effectiveness, but they have not approved use of any foreign vaccine.
"As you can imagine, my family and I miss my father enormously," the Prince of Wales said during his emotional appearance.
The 99-year-old Duke of Edinburgh took part in designing the modified Land Rover that will carry his coffin.
The Duchess of Sussex did not get medical clearance to travel alongside her husband.
The La Soufriere volcano covered parts of the Caribbean island in ash and forced thousands to evacuate.