​A new chapter for Sienna Miller

In the 2006 movie "Factory Girl," Sienna Miller played the role of Edie Sedgwick, the socialite caught up in the pop art world of Andy Warhol. She plays a very different role in her latest film, as Anthony Mason shows us in this Sunday Profile:

For much of her career, Sienna Miller was known more for her tabloid headlines than her acting roles. That may be about to change.

The British actress, who grew up in London, has seven films in the works.

Among them: the upcoming comedy, "Unfinished Business," in which she plays Vince Vaughn's former boss, now business rival.

She's also in the new Clint Eastwood film, "American Sniper," about Navy SEAL sharpshooter Chris Kyle, played by Bradley Cooper. Miller plays his wife, Taya.

"Do you view this kind of as a second act?" Mason asked.

"I think its impossible not to," she replied. "Maybe not a second act, because I'm 32 and I feel a little young for a second act! But, you know, a nice new chapter for sure."

Actress Sienna Miller with director Clint Eastwood during filming of "American Sniper." Warner Brothers

She was just 21 when she won her first major film roles in 2003, playing mobster Daniel Craig's girlfriend in "Layer Cake," and then one of Jude Law's flings in "Alfie."

The chemistry between the costars was real; a romance blossomed on the set, and Law and Miller quickly became the paparazzi's favorite couple.

"You were pretty young when your private life basically became your public life," said Mason. "How did you cope with that?"

"I think I've always been kind of a resilient person," Miller replied. "It just was -- that was my life. And it coincided with a very exciting time. I was falling in love with someone and it was great."

Actress Sienna Miller with correspondent Anthony Mason in New York City. CBS News

But their love affair became a soap opera, when Law was caught cheating with his children's babysitter, and Miller broke off their engagement. She was hounded by photographers everywhere she went.

Mason asked, "What was the cost to you of all that?"

"I think it was incredibly damaging in terms of my career," she said. "It's very hard to be considered a serious actor if you have that level of paparazzi attention or tabloid attention."

"Do you think it cost you roles?"

In Clint Eastwood’s new film “American Sn... 04:23

"I do. Yeah, I do. And I understand why. It became inelegant. It became completely out of control. It was a daily -- you know, I was sick to death of me!"

But the paparazzi weren't -- and intimate details of Miller's life began turning up in the tabloid News of the World.

She began suspecting her friends and family: "Yeah, of course, because it felt ridiculous to think, 'Well, someone's hacking my phone.' It just sounded dramatic and odd."

Then it broke that the newspaper owned by Rupert Murdoch's News International had been routinely hacking into the cellphones of celebrities, politicians and members of the royal family.