The adorable moment was caught on camera showing Kate, 38, breaking into a warm smile before accepting the flower and appearing to thank her husband.
The duke and duchess were welcomed by a drummer as they arrived at the Bradford Khidmat Centre for their third engagement of the day, after meeting youngsters at City Hall and making milkshakes at a restaurant.
Reportedly, the Duchess of Cambridge wanted her children Prince George, six, Princess Charlotte, four, and Prince Louis, one, to spend more time with Meghan Markle and Prince Harry's son Archie Harrison, who was born on May 6 past year. While they aren't the first to step back from their positions as royals, they are the first to want to keep one foot in the door.
Kate and William share sons Prince Louis, 1, Prince George, 6, and daughter Princess Charlotte, 4. I tried to knit him a very special jumper, but I got half way down and it splattered.More news: Global PC market records positive growth for the first time since 2011
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Meghan has flown to Vancouver, leaving Prince Harry to meet the Queen and talk through their decision. Before the summit could begin, Prince Philip could be seen being driven out of the Sandringham estate on Monday.
A firestorm of attention has followed the Duke and Duchess of Sussex' decision.
Today was the couple's first joint public engagement together since a charity event in London two months ago on November 12 for their volunteer text support service Shout. We look forward to sharing the full details of this exciting next step in due course, as we continue to collaborate with Her Majesty The Queen, The Prince of Wales, The Duke of Cambridge and all relevant parties.More news: Jennifer Lopez wants a simpler life
The duke said: "Poor Tom, it's a terrible injury".
"After many months of reflection and internal discussions, we have chosen to make a transition this year in starting to carve out a progressive new role within this institution", the pair wrote.
Catherine looked elegant, as always, for the outing as she wrapped up against the cold British winter weather in a stunning deep green coat by British fashion house Alexander McQueen.
Underneath the coat, Kate wore a black and white tartan pattern pussybow dress from high street retailer Zara, which she paired with black pointed court style heels, a small black bag and gold drop earrings by Zeen.More news: Kim Kardashian Packs Into Barely There Pink Bikini, "About To Pop Out"
The shelter posted a photograph of the duchess's visit this week.