New York ? Kate Burton called her agent last August with a simple question: Where were all the acting jobs?

Sure, she had a role in a pilot for a new medical drama on ABC and, yes, there were recent guest spots on “Law & Order” and “The Practice.” Still, for an actress of Burton’s pedigree – she’s the daughter of Richard Burton and was one of only three actors to be nominated for two Tonys in the same year – it was an unusually slow time.

Oh, how things have changed.

Less than a year later, the pilot has turned into the hit “Grey’s Anatomy,” Burton was part of the starry cast of the HBO miniseries “Empire Falls” and, perhaps most dear to her heart, she now has her largest role yet on Broadway – the title character in the revival of W. Somerset Maugham’s “The Constant Wife.”

“I had no idea that everything would come out at the same time,” she said recently, looking casual in shorts, a sleeveless shirt and a tan sun hat on a stifling day in Manhattan.

“Empire Falls” was shot about a year and a half ago, and Burton never expected “Grey’s Anatomy” to become a hit when the pilot was filmed with her in the role of the ailing Dr. Grey. As for “The Constant Wife,” Burton wasn’t even planning to be in New York this summer until Todd Haimes, artistic director of the Roundabout Theatre Company, called her about the role of Constance Middleton.

Long stretch

It had been about 2 1/2 years since Burton last appeared on the New York stage in a major production (David Mamet’s “Boston Marriage” at the Public Theater), and her husband, Michael Ritchie, is now the artistic director of the Center Theatre Group in Los Angeles.

Sitting in the Calvin Klein store on Madison Avenue after a recent dress fitting, the 47-year-old Burton said she couldn’t pass up the challenge of playing Constance, who chooses an unorthodox method to deal with her husband’s infidelity. Once she learned Lynn Redgrave was set to play her mother and the rest of the cast would be filled out with stalwarts of the New York stage, “it was if I had died and gone to heaven.”

Challenging dialogue

Yet, while the fact that “The Constant Wife” is a comedy interested her after a run of dramas, the sheer number of lines was, at first, intimidating.

“I really was in a state of abject fear for about, I would say, 10 days to two weeks,” Burton said. “The lines were sort of clicking but not totally.”

The play’s director, Mark Brokaw, jokes that it should be called “The Constantly Talking Wife,” and Redgrave said with a laugh that “we never hesitate to remind” Burton that she always seems to be making a speech when she is on the stage.

However, Maugham’s sometimes ornate language – the play is set among the upper class in 1926 London – can certainly be challenging to master.

Once Burton was able to master lines such as “Do you mean that I ascribe to your perfect manners what was only due to your stupidity?” she could get back to simply enjoying the chance to work with a gifted ensemble, which includes Michael Cumpsty as her philandering husband and John Dossett as a former beau who returns to the scene.