SAGAPONACK, N.Y. – Bill and Hillary Rodham Clinton are renting a virtual Shangri-La in this lush, beachside paradise in the Hamptons. The $11 million mansion sprawls over 3.5 acres of prime real estate, with four fireplaces, six bedrooms, a heated pool and private path to the beach.

But Clinton vacations are not about kicking back.

Hillary Clinton will be spending many hours here holed up in an office, though one with an ocean view, working on a memoir about her days as secretary of state, people close to the family say.

And, not one day after arriving here late last week, Bill Clinton was making a public appearance, at a softball game played each summer between artists and writers in East Hampton. There he found himself deluged by news photographers and autograph seekers as "Today" show host Matt Lauer and The Daily News Publisher Mortimer B. Zuckerman looked on.

A reporter asked, Was he getting to relax? "Apparently not," he joked.

Relaxation is not entirely the point when the Clintons head to the Hamptons, where work and play are inexorably intertwined. Since they arrived, Bill Clinton celebrated his 67th birthday at the rented mansion with Paul McCartney and Jimmy Buffett. And the couple has entertained Marty Markowitz, the Brooklyn borough president, an early supporter of Hillary Clinton’s 2008 presidential bid.

On Friday, there will be a Bill, Hillary and Chelsea Clinton Foundation fundraising gala at Topping Rose House – a new hotel-restaurant operated by celebrity chef Tom Colicchio. Attendees will include Revlon Chairman Ronald O. Perelman, an event "chairman," requiring a $50,000 donation; and Zuckerman and the real-estate executive Peter S. Kalikow, event "co-chairs" at the $25,000-donation level.

The Clintons are known for keeping busy: in the last house they rented, an eight-bedroom, wood-shingled place on Georgica Beach, the former president spent time rearranging the books in the house by subject matter.

"He had organized it in a very effective way," the house’s owner, Elie Hirschfeld, recalled.

The Clintons have filled their rental this summer with extended family, including Bill Clinton’s half-brother Roger and his son, Tyler. Hillary Clinton’s brother Tony Rodham is also in Sagaponack. He brought his son, Zach, from his first marriage and his younger children, Simon and Fiona, from his second marriage. The former president took Simon and Fiona mini-golfing Wednesday night.

The Clintons’ daughter, Chelsea, and her husband, Marc Mezvinsky, will not be coming. She is in Oxford, England, finishing her dissertation; he is in New York working on a business deal.

The Clintons, who are here for roughly two weeks, have been coming to the Hamptons for so long – as visitors, cash-seeking candidates and, more recently, renters – that they have built up a social circle, and with it, some social obligations.

"At this point, he knows a lot of people who happen to summer out here," said Alan Patricof, an investor who is a longtime family friend and fundraiser.

But the couple, he said, get all the privacy they want.

Indeed, they are left alone during morning walks on the beach with their dogs. (They now have three: Seamus, an 8-year-old arthritic chocolate Labrador; Tally, a poodle; and a new companion, Maisie, a curly-haired pup of undetermined breed.)

They have made Babette’s, an easygoing French restaurant with an outdoor porch, a regular spot for cake, and usually sample the menu of Almond restaurant in Bridgehampton, which is owned in part by Jason Weiner, the brother-in-law of Hillary Clinton’s aide Huma Abedin.

They have been known to take in a show at the Stephen Talkhouse, the small, beach-shack-like music club in Amagansett that has drawn appearances from Bo Diddley, Van Morrison and Paul Simon. In 2011, they were tipped off that Buffett would make a surprise appearance at a show headlined by a Cape Verdean performer, Ilo Ferreira.

But their visit gave a scare to their Secret Service detail when residual damage from Tropical Storm Irene caused power to go out temporarily in the cramped nightclub. "There was a loud pop and then total darkness," the owner, Peter Honerkamp, said. After five seconds, he said, the lights came back up and "everyone laughed, breathed a sigh of relief, and the show went on."

The Clintons, in fact, were among those who refused to let the storm drive them out of the Hamptons that August. They have been through plenty worse.

As the storm loomed, recalled Hirschfeld, the owner of the rental, he went out to check on the house and make sure everything was battened down.

The Clintons were there, he said, and they made clear they were enjoying his home’s amenities. But, he added, they were both working, too – he on a book, she on business related to the State Department.

"He had taken the dining room as his work space, and she had taken this study-library as hers," Hirschfeld said. "He told me very proudly that he enjoyed being here and the setting and everything helped him complete his book. He finished it in the dining room." (That would apparently be his 2011 book, "Back to Work," his prescription for economic renewal.)

Bill Clinton declared that the family was staying put. He had heard the sea was expected to rise about 13 feet, and he had personally measured the dune at the edge of the property at 16 feet.

"I was astonished at his level of detail," said Hirschfeld, who admitted he never knew how tall his dune was. "My office checked the survey, and indeed the president was correct."

Bill Clinton then reviewed the details of the emergency generator and which house functions would continue if the power went out.

The Clintons moved on from Hirschfeld’s house this summer, in part because of the high cost of maintenance and utilities, which ate up much of their security deposit from the $200,000 rental. This year, they have moved several miles west, to Sagaponack.

This summer’s rental – which is costing them about the same, according to people with knowledge of their arrangement – is owned by Michael Saperstein, an investment banker who happens to be a donor for their opponents, the Republicans.

That sort of thing, of course, is unavoidable in a place so rife with political contributors. In fact, the day after the Clinton foundation gala, on Saturday, former New York Mayor Rudolph W. Giuliani – who was competing with Hillary Clinton for a Senate seat in 2000 before he dropped out of the race – will be a host of a fundraising event in nearby Southampton for someone who could be her opponent in the 2016 presidential race, Gov. Chris Christie of New Jersey.

For now, those who consider themselves both friends and donors say they are not going to push the whole 2016 thing this vacation.

"It’s not about politics, it’s not about government; they’re welcomed as friends," said Robert Zimmerman, a prominent Democratic fundraiser who has a home in Southampton.

But not everyone here has gotten the memo. Even at the softball game Saturday, as Bill Clinton made his way across the field, shouts like "We’ll see you back in the White House!" could be heard.

© 2013 The New York Times Company