The couple was spotted packing on the PDA during an afternoon stroll together over the weekend. The Game of Thrones star and McDowell were seen walking arm-in-arm as they went grocery shopping in Venice, California.
At one point, the director, 35, leaned in for a kiss as they walked down the street.
After grabbing a few groceries, the two treated themselves to frozen yogurt and health shots.
The romantic outing comes just weeks after the couple seemingly confirmed their relationship on social media.
While celebrating her 32nd birthday, Clarke shared a photo of two shadows in the sand, with one kissing the other on the cheek.
“Well that was a birthday I won’t be forgetting in a while,” she captioned the photo, adding a heart emoji.
And while Clarke didn’t tag McDowell in the post, the director shared the same photo on his own Instagram.
“Happy birthday, E,” he wrote, also including a heart emoji.
McDowell was previously linked to actress Rooney Mara back in 2012. The filmmaker is the son of legendary British actor Malcolm McDowell and Oscar-winning actress Mary Steenburgen, and the stepson of The Good Place‘s Ted Danson.