Hillary Clinton was on Martha’s Vineyard on Sunday, July 21, the day President Biden dropped out of the presidential race, when her phone rang. Her husband, former President Bill Clinton, had already received a call from the same number, so she knew who wanted to talk to her.

Vice President Kamala Harris was calling to tell her she was running for president and hoping to build support as quickly as possible. Mrs. Clinton didn’t hesitate: She told the vice president she was all in. The Clintons rushed out an endorsement well ahead of many other party leaders, including the Obamas.

As Democrats revolted against Mr. Biden’s re-election bid this summer, Mrs. Clinton wanted no role in pushing him out, according to people briefed on her thinking. But behind the scenes, she was also adamant that if the president chose to step aside, Ms. Harris should become the party’s nominee with no drawn out primary.

The two women, once on opposite sides during the contentious 2008 Democratic primary, have quietly bonded over the past several years, sharing dinners at Mrs. Clinton’s Washington home, discussing high-impact decisions like whom Ms. Harris should pick for her running mate, and connecting over the still-stubborn ways that women in high office can be underestimated.

On Monday night, Mrs. Clinton, who came achingly close to becoming the nation’s first female president, will pass the torch to a woman nearly two decades younger, in a moment that friends say comes with a mixture of bittersweetness and pride for Mrs. Clinton.

The last time Mrs. Clinton stood on the convention stage, dressed in suffragist white, she thought she was on track to be the next president. Much has happened since then — from Mrs. Clinton’s grief over and eventual acceptance of her 2016 loss, to the rise of a new generation of Democratic leaders. And America seems more at ease with women as candidates for the highest office, a shift no doubt advanced by Mrs. Clinton’s candidacies.

But still her party is grappling with the energized movement Donald J. Trump created. The former secretary of state is acutely aware of how challenging it will be to defeat Mr. Trump, and the ugliness of the personal attacks that await Ms. Harris.

“Nothing would make Hillary happier than seeing the first in history beat the worst in history,” said Philippe Reines, a former top adviser to Mrs. Clinton who has been playing the role of Mr. Trump in Ms. Harris’s debate prep.

Mr. Reines said a Harris victory in November would be a “karmic twofer” for Mrs. Clinton — who longs for Mr. Trump’s defeat and would find it more satisfying if Mr. Trump lost to a woman.

Of course, Mrs. Clinton’s presence triggers uncomfortable flashbacks for some Democrats who were devastated by her loss. But many are leaning into the present, watching the stunning reversal in energy for their party since Mr. Biden bowed out, and allowing themselves to feel hopeful — and excited — once again.

“After the disappointment in ’16, I think many, many of us had P.T.S.D. — I know I did,” said Susie Tompkins Buell, a longtime friend of Mrs. Clinton’s and a major Democratic donor who is supporting Ms. Harris. “I’ve never been the same. And suddenly I feel a certain invigoration that I have not had in a long time.”

Indeed, alumni from both Hillary and Bill Clinton’s former campaigns plan to gather for a reunion in Chicago on Monday.

For Mrs. Clinton personally, the chain of events that led to Ms. Harris’s rise has made it easier to enthusiastically — rather than dutifully — back her. Two people close to her described the speech she is expected to deliver on Monday as upbeat and focused on the work ahead.

Mrs. Clinton herself, they said, is in “happy warrior” mode, thrilled that Ms. Harris appears to be pulling ahead of Mr. Trump in national and battleground-state polls.

Mr. Trump’s ongoing political strength, people close to Mrs. Clinton said, has helped reset widespread beliefs about her 2016 defeat — the idea that only Mrs. Clinton, with all of her baggage and well-documented political weaknesses, could have lost to such a candidate, and that had she only visited Wisconsin, history would have changed course. The ensuing years have shown Mr. Trump to be a unique and durable political force.

Ms. Harris, after all, has ascended because Mr. Biden was pushed out by fellow Democrats who feared he, too, would lose to Mr. Trump and bring the party down with him.

Mrs. Clinton, who worked through her searing defeat with hikes in the woods with her dogs and bingeing on bad television, has assumed a place as an admired stateswoman in her party. She is planning a 10-city national book tour starting in September for her latest book, “Something Lost, Something Gained: Reflections on Life, Love, and Liberty,” which will serve as a way to speak to large audiences as an unofficial surrogate for the Harris campaign.

“She wants to help, she wants to win, and she’s ready to do whatever the campaign asks,” said Nick Merrill, a spokesman for Mrs. Clinton.

The two women didn’t have much of a relationship before 2020 and Ms. Harris’s ascension to the vice presidency. They were on opposite sides of the 2008 presidential primary between Barack Obama and Mrs. Clinton. Ms. Harris was among the first Democratic elected officials to endorse the Illinois senator and worked hard for his election.

Still, Mrs. Clinton has said that she feels a particular kinship with Ms. Harris because they are both lawyers who chose at the beginning of their careers to work on issues related to families and children. Mrs. Clinton’s first job after law school was as a staff lawyer for the Children’s Defense Fund, while Ms. Harris worked in the Alameda County District Attorney’s Office, specializing in prosecuting child sexual assault cases.

And since the beginning of the Biden administration, Mrs. Clinton has used her stature to quietly bolster Ms. Harris. She blames many things for her 2016 defeat. But after James B. Comey, the former F.B.I. director, sexism ranks high on the list. In Mrs. Clinton’s view, to be a woman in the top tier of national politics is to at times be undervalued and underestimated.

When she witnessed it happening to Ms. Harris, she hosted multiple dinners for her at Whitehaven, the Clintons’ mansion just a stone’s throw from the vice president’s residence at the Naval Observatory. The dinners were casual buffet-style affairs but also strategic.

Mrs. Clinton invited Washington veterans whom she trusted and who could talk with Ms. Harris — like Rahm Emanuel, the former White House chief of staff; Jennifer Palmieri, the longtime political operative who worked for both Clintons and is now advising Ms. Harris’s husband, Doug Emhoff; the veteran Democratic strategists Paul Begala and Karen Finney,; and Douglas Elmendorf, the former dean at Harvard Kennedy School.

That helped cement the relationship, which continued in other ways, as Mrs. Clinton made a visit to Ms. Harris at the White House, and they spoke on the phone to discuss foreign policy before the vice president’s first international trip.

When the two saw each other most recently at the Houston funeral for Representative Sheila Jackson Lee, they discussed Ms. Harris’s running-mate decision. Ms. Harris called Mrs. Clinton the next weekend to continue the conversation, according to a person briefed on the call.

And they have increasingly relied on an overlapping set of aides. Ms. Harris’s chief of staff, Lorraine Voles, worked for Mrs. Clinton in the Senate. The debate prep sessions that include Mr. Reines are being overseen by Karen Dunn, another longtime “Hillary world” figure who ran Mrs. Clinton’s debate prep. Ms. Harris’s communications director, Brian Fallon, served in the same role for Mrs. Clinton on her 2016 bid, and Ms. Harris’s sister and adviser, Maya Harris, worked for the Clinton campaign as a top policy aide.

Mrs. Clinton’s allies say she has also helped Ms. Harris in a less tangible way: by helping Americans imagine a woman president.

“It helped open doors and change perceptions,” said Senator Debbie Stabenow, a Michigan Democrat. “Every time a woman does that, it just makes it easier for the next woman to be able to be judged on her own merits.”

In her speech, Mrs. Clinton is expected to speak less about Mr. Trump, although she wants to address the attacks he has been making against Ms. Harris, and more about what Democrats can do when they come together.

If Mrs. Clinton and her allies see this moment as, in some ways, an extension of her own rise, there are limits to the parallels.

Mrs. Clinton, now 76, has long been aligned with the political establishment. Ms. Harris, 59, is seeking to build a campaign focused on the future, and represents a generational change from Mr. Biden and Mr. Trump, who, along with Mrs. Clinton, were all born in the 1940s.

While Mrs. Clinton leaned into the historic significance of her candidacy (one 2016 campaign slogan was “I’m With Her”), Ms. Harris, who as a Black and South Asian woman is a barrier breaker several times over, has rarely emphasized her identity, playing up her credentials as a former prosecutor instead.

Their paths to elected office were also starkly different. Before Mrs. Clinton became the first woman elected senator from New York, she was best known nationally as a first lady — first of Arkansas, where Mr. Clinton was governor, and then of the country.

Ms. Harris, by contrast, did not marry until she was nearly 50 and serving as California’s attorney general. Her husband — Mr. Emhoff — would become the nation’s first first gentleman if she wins.

Still, the through line from one candidacy to the other is hard to deny.

Last week, Megan Rooney, a speechwriter, left her job at the White House to join Ms. Harris’s team and will help draft her convention address for Thursday night.

It was Ms. Rooney who in 2016 stayed up all night to help write Mrs. Clinton’s painful concession speech after her stunning defeat.

“I know we have still not shattered that highest and hardest glass ceiling,” she wrote for Mrs. Clinton eight years ago, “but someday someone will — and hopefully sooner than we might think.”

Maya King contributed reporting.