Kate Middleton and Prince William are continuing their royal duties with a visit to the Scottish Isles.

The Prince and Princess of Wales, both 44, traveled to the Isle of Bute in Scotland on Thursday, Sept. 17. They visited their namesake town of Rothesay, a meaningful location as the couple holds the Scottish titles of Duke and Duchess of Rothesay.

The day of outings marks the first official visit by William and Kate to the island after visiting the Isles of Mull and Iona last year.

Prince William and Princess Kate’s visit is meant to highlight the power of community, connection and volunteering.

On their first engagement of the day, Willian and Kate headed to Bute Shinty Club in Rothesay, where shinty, one of Scotland’s oldest traditional sports, has been played for generations. The club, a vital part of life on the island, was founded in 1946 and is run entirely by volunteers, many of whom are former players.

They stepped out in coordinating ensembles, with Princess Kate wearing an olive green turtleneck sweater while Prince William wore a jacket in a similar shade.

Both William and Kate had a go at hitting a ball with a curved wooden stick called a camán. The Princess of Wales, who grew up playing field hockey, missed on her first attempt before making a strong connection, earning applause from those gathered.

Meanwhile, Prince William laughed when his first attempt didn’t send the ball very far, but he hit hard on his second try.

The couple’s second stop brought them to Ettrick Bay to meet the team behind Beachwatch Bute and learn about their efforts to protect and preserve the island’s coastline.

At Ettrick Bay, one of Bute’s most picturesque beaches, the couple joined a beach ranger and other supporters of the charity during a beach clean-up, picking up trash while they heard about the community’s role in safeguarding the local environment.

During their day of outings, they will spend time with locals, including visiting the community-owned Anchor Tavern Pub to hear about the importance of everyday interactions.

Their outing in Scotland comes after the return of Prince William’s estranged brother, Prince Harry, and Harry’s wife, Meghan Markle, to the U.K. last month.

Royal author Simon Vigar tells PEOPLE that William and Kate are relying on an age-old royal philosophy when it comes to the Duke and Duchess of Sussex’s move back to Britain: “It is keep calm and carry on. They see it as a sideshow and ancient history.”

The Prince and Princess of Wales have kept things focused on their family and their royal work. This month, they accompanied Prince George as he began his studies at Eton College. They have also stepped out for multiple royal engagements, including a joint appearance in support of one of William’s mental health initiatives on World Suicide Prevention Day.

“They are shining a light on things that are important to them,” says Ailsa Anderson, the late Queen Elizabeth’s press secretary in this week’s PEOPLE cover story. “What they don’t want is all this other noise becoming a distraction.”

PEOPLE understands that King Charles and Harry have spoken at least once since the Sussexes’ arrival back in Britain, but have not seen each other. William and Harry, meanwhile, remain estranged.

“William’s view is clear — any relationship his father has with Harry or the Sussexes as a family is entirely up to him,” says Russell Myers, author of William and Catherine. “But looking toward the future, he will have no relationship with them, in a working or private capacity whatsoever.”

“It will be incredibly draining,” adds royal historian Amanda Foreman. “They will always have to look over their shoulders and factor them in. And all they can do is deflect. Yet, they’ll get lots of jabs and questions: ‘When are you going to make up with your brother?’ ”

Vigar wonders whether next year’s 30th anniversary of Diana’s death could eventually provide an opportunity for her sons to reconcile.

“Diana would have hated all this and would have banged their heads together and wouldn’t have allowed [the rift] to happen,” he says.

“It’s clearly incredibly difficult. The trust has broken down,” says Anderson. “Let’s hope it’s not broken completely, and there’s a chink in the armor on both sides, and there could be some sort of reconciliation. But that’s not happening anytime soon.”