WASHINGTON—As the administration’s most ardent senior-level advocate of securing a cease-fire in Gaza, Vice President Kamala Harris ’s elevation to the Democratic Party’s standard-bearer now puts her in a stronger position to advocate for a shift in U.S. policy toward Israel and to carry out those changes should she win in November.

Though Harris has been careful not to contradict Biden, she has often pushed the envelope of the administration’s messaging on the Israel-Gaza conflict . She has at times advocated forcefully, and ahead of other administration officials, for limiting civilian casualties and addressing the humanitarian crisis in the enclave.

 “ I think she will be more inclined to find other ways to put pressure on Israel if the situation in Gaza does not dramatically improve,” said Ivo Daalder , who served as NATO ambassador during the Obama administration and is well connected with Biden aides.

Harris’s Middle East views will be in the spotlight this week when she and Biden meet with Israeli Prime Minister Benjamin Netanyahu . The plan is for Harris to have her own separate meeting with the Israeli leader, according to an aide to Harris. She won’t be in Washington for his high-stakes speech to Congress because she will be traveling to Indianapolis for a previously scheduled event.

During the meeting, Harris is expected to tell Netanyahu that “it is time for the war to end in a way where Israel is secure, all hostages are released, the suffering of Palestinian civilians in Gaza ends, and the Palestinian people can enjoy their right to dignity, freedom, and self-determination,” the aide said.

Harris is likely to focus on securing the nomination this week and will want to steer clear of any confrontation with Netanyahu, analysts said, not least so as to avoid opening herself up to any criticism that she is weak on Israel.

Harris’s relationship with Netanyahu will be very different than that of Biden, who has sparred with the Israeli prime minister but also has decades of experience in dealing with him, a U.S. official said.

She won’t be starting from scratch. Harris has been on almost every call between Biden and Netanyahu, for a total of more than 20, according to the White House official.

She also has a longstanding relationship with Israeli President Isaac Herzog , the official said. The two have had five phone conversations since Oct. 7 and met once in person at the Munich Security Conference, the official said.

Her husband, Doug Emhoff, is the first Jewish spouse of a U.S. president or vice president and has been outspoken on the issue of antisemitism particularly since the Oct. 7 attacks.

A Harris presidency could lead to a shake-up of the Democratic national security team, with Philip Gordon, her national security adviser, likely to play a central role. Gordon served as the top State Department official for Europe in the Obama administration and later worked as a senior White House official on Middle East issues, where he was deeply skeptical of plans to arm Syrian opponents of Syrian President Bashar al-Assad .

Key Biden appointees, including national security adviser Jake Sullivan, Secretary of State Antony Blinken and Defense Secretary Lloyd Austin wouldn’t likely be extended in their current roles, current and former officials say.

Over several decades, the Democratic foreign policy establishment has been divided between those seeking a more assertive role for the U.S. abroad, and others more skeptical of military force. The Clinton administration dubbed the U.S. an “indispensable nation” and undertook selective military interventions to quell ethnic strife in the Balkans, while the Obama administration was more cautious about the use of force and balked at providing lethal military assistance to Ukraine.

As vice president, Harris hasn’t had an opportunity to define her own brand of foreign policy, though some observers say she might ultimately align herself more closely with the progressive elements of the Democratic Party and might be more inclined to make U.S. support for Israel more conditional on its conduct in Gaza and the West Bank.

Harris drew attention during a March speech in Selma, Ala., when she assailed what she described as inhumane conditions in the enclave, and urged Israel to do more to expedite aid to Gaza. She talked in graphic terms about how Palestinians in Gaza were eating animal feed and leaves to stay alive.

“Our common humanity compels us to act,” she said.

Jim Zogby , the founder of the Arab American Institute, who has criticized Biden’s response to the war, said he spoke with Harris by phone in October and believed she has demonstrated “far greater empathy” for Palestinians than Biden and other White House aides.

Early on during the war, Harris’s advisers were concerned about “Biden’s Bibi bear hug,” said Steven Cook of the Council on Foreign Relations, arguing that it wasn’t buying them important influence.

“She is a moderate, but I think the earlier and more vocal criticism of [Netanyahu] was her nod to progressives,” Cook added.

Gordon, Harris’s national security adviser, noted in a June address in Israel that the “U.S.-Israel partnership has been tested, perhaps as never before.”

Defending the multiphase cease-fire deal that Biden announced in May, Gordon warned that a rejection of this approach by Israel wouldn’t pave the way for total victory but “would lead to endless conflict, draining Israel’s resources, contributing to its global isolation, and preventing the hostages from being reunited with their families.”

During her years in Congress, Harris was known more for her views on domestic issues than foreign policy. She served on the intelligence and homeland security committees, where she emerged as a reliably liberal vote against military intervention in Yemen, arms sales to Gulf states, and former President Trump’s nominees for senior national security positions.

Write to Michael R. Gordon at michael.gordon@wsj.com and Lara Seligman at lara.seligman@wsj.com