Hillary Clinton Is Not a Candidate. She Looms Over 2020 Anyway.

But as Ms. Klobuchar saw, those who cross the Clintons risk blowback.

Ms. Gillibrand and Mrs. Clinton were not on speaking terms ahead of Ms. Gillibrand’s run, even though Mrs. Clinton had inspired Ms. Gillibrand to get into politics, wrote the foreword to her book and campaigned for her in her first House race. Their relationship deteriorated after Ms. Gillibrand in late 2017 said a resignation by Mr. Clinton would have been “appropriate.”

In an interview in January, Ms. Gillibrand gingerly said she planned “to reach out” to Mrs. Clinton: “I would like to hear her perspective and I would be very grateful for her advice.” Later, she added: “I value her counsel. I hope I will be able to earn that in the future.” The two are now supposed to meet soon, according to a person familiar with the matter.

Those who have spoken with Mrs. Clinton say she has plenty of advice. After running a campaign that published a 288-page policy book, she urges candidates not to let their message get clouded by wonky policy debates. As a politician who famously claimed a “vast right-wing conspiracy,” she has warned about the barrage of Republican attacks they are likely to face. She has specifically warned female candidates of the gendered expectations they will face, in particular on national security. And she has encouraged everyone to preserve their health amid the rigors of campaigning, a struggle for Mrs. Clinton, who found her campaign derailed by conspiracy theories about her physical fitness after she fainted at a 9/11 memorial ceremony.

In conversations with the Democratic National Committee chairman Tom Perez, she has urged the national party to fund-raise more aggressively and build a data-sharing program for its candidates that is comparable to the one Republicans successfully leveraged on behalf of Mr. Trump in 2016, according to some who have spoken with her, including Mr. Perez.

“She had a lot of advice,” Mr. Hickenlooper said. “She’s been there. It’s one thing to read about stuff and it’s another thing to live it. She is very insightful about drawing wisdom from her experience.”

As they turn their focus to a 2020 rematch against Mr. Trump, Democrats are determined not to repeat what they see as the missteps made by Mrs. Clinton and her campaign.

“I begin by acknowledging that Hillary Clinton beat Donald Trump by millions of votes,” Mr. Castro said. “At the same time, it’s clear we want to go with a laser focus on winning back Florida, Pennsylvania, Michigan and Wisconsin.”