The couple, who have been married for more than 10 years after meeting at St Andrews University, rarely put on public displays of affection.
Another shot shows Kate draping her arm around William.
At the ceremony, which took place earlier this week at Alexandra Palace in north London, the Duchess presented an award while the Duke made a speech about the impact of climate change and the importance of protecting the environment.
He issued a rallying cry at the inaugural ceremony on Sunday to the next generation to keep on “demanding change” as innovative green projects from across the globe were awarded £1 million.
At the end of the event, televised by the BBC, William took to the stage to tell the audience: “I want to say something to the young watching tonight.
“For too long, we haven’t done enough to protect the planet for your future, the Earthshot is for you.
“In the next 10 years, we are going to act. We are going to find the solutions to repair our planet.
“Please keep learning, keep demanding change, and don’t give up hope. We will rise to these challenges.”
The younger generation has been inspired by the actions of climate change activist of Swedish teenager Greta Thunberg, who first started her Friday protests outside her country’s parliament in August 2018, inspiring children across the world to stage school strikes.
Harry Potter star Emma Watson, wearing a wedding dress made of 10 dresses from Oxfam, and Dame Emma Thompson were among those who trod the ceremony’s green carpet.