Emilia Clarke and Director Charlie McDowell Spark Romance Rumors with Flirty Instagram Photo

Does Emilia Clarke have a new man in her life?

The Game of Thrones actress seemingly confirmed her romance with director Charlie McDowell on Wednesday with a flirty Instagram post.

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 an emoji heart to the end.

And while Clarke didn’t tag McDowell in the post, the director shared the same photo to his own social media account.

“Happy birthday, E,” he wrote, also including a heart emoji.

A rep for Clarke did not immediately return PEOPLE’s request for comment.

McDowell was previously linked to actress Rooney Mara back in 2012. The 35-year-old 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.

Along with the romantic beach trip, Clarke rang in her birthday with a Games of Thrones-themed birthday cake.

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“FULL DISCLOSURE: dragons are not for eating. Only for riding, and the occasional bbq,” she captioned a photo of herself holding a cake decorated with a dragon on top. “But dear instaworld I wanted to say a huge thank you to all you glorious wonder creatures who wished me a happy birthday! I felt like one very lucky chica to have been sent so much love.”