The Oscar winner appears "very, very together" with British lawyer, an observer tells PEOPLE
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Has George Clooney jumped back into the dating game?

After splitting with Stacy Keibler last July, Clooney, 52, attended a special screening of his latest movie, The Monuments Men, at the White House on Feb. 18 with President Barack Obama. And he brought British lawyer Amal Alamuddin, 36, as his personal guest.

“They were holding hands,” says Harry Ettlinger, 88, one of the World War II soldiers whose efforts to recover stolen art from the Nazis inspired the film.

The Oxford- and NYU-educated Alamuddin, who speaks three languages and was voted No. 1 on London’s “Hottest Barrister” list in 2013, “is a beautiful lady,” Ettlinger tells PEOPLE. “I said to myself, ‘George, you did a lot of good things and you sure know how to pick them!'”

After the screening, Alamuddin – who represents WikiLeaks founder Julian Assange – joined Clooney and his costars Bill Murray and Matt Damon at the Willard Hotel’s Round Robin & Scotch Bar for a night cap.

“His arm was around her shoulder and she had hers around his,” an observer tells PEOPLE. “They just seemed very, very together.”

“They were stuck like glue,” adds the observer.

Clooney and Alamuddin first sparked relationship rumors last October, when they were seen dining together at London’s Berners Tavern.

“She was flirting like crazy while he was just playing it cool,” an onlooker said at the time.

Clooney, who was also linked with several other women at the time, subsequently denied the two were an item, telling PEOPLE exclusively, “Three different stories in three weeks. I should be an athlete. But, no of course, it’s all made up.”

Since then, the actor has not commented on his relationship with Alamuddin. But in December he told W magazine that when it comes to the love of his life, “I haven’t met her yet.”