Ms. Harris and Mr. Biden usually begin the day receiving the President’s Daily Brief together in the Oval Office, a tradition reinstated since the departure of President Donald J. Trump, who had little interest in it. They also quickly embraced the idea of a weekly lunch in the White House as a private opportunity to build trust and share thoughts.

In building her own staff, Ms. Harris selected people who she knew had good relationships with the president and his team. She chose Tina Flournoy, who has close ties to Mr. Klain, to run her office. Ashley Etienne, a former adviser to Speaker Nancy Pelosi, is her communications director.

Ms. Harris also knew that the president held Symone Sanders, who worked as press secretary to Senator Bernie Sanders’s 2016 presidential campaign before joining the Biden campaign, in high regard. Ms. Sanders is now her press secretary.

Aides to the vice president repeatedly stressed that all of her public events and messages were closely coordinated with members of Mr. Biden’s team. A visit by Ms. Harris last week to the National Institutes of Health to thank scientists and receive her second dose of the coronavirus vaccine was paired with a speech later in the day by Mr. Biden in which he announced the acquisition of 200 million additional doses of the vaccine.