In Afghanistan, several officials said, Mrs. Clinton hungered for a success on the order of the Dayton Accords, which ended the Bosnian War. But when her special representative, Richard C. Holbrooke, who had negotiated that agreement, fell out of favor with the White House and later died, those dreams died with him.

Then came the Arab awakening . . . and it plunged Mrs. Clinton into a maelstrom. It tested her loyalty to longtime allies like President Hosni Mubarak of Egypt and reinforced her conviction that anger at decades of stagnation, fueled by social media, would sweep aside the old order in the Arab world.

After Britain and France argued for intervening to defend Libya’s rebels against Col. Muammar el-Qaddafi, Mrs. Clinton played an important role in mobilizing a broad international coalition and persuading the White House to join the NATO-led operation.

But it was Syria that proved to be the most difficult test. As that country descended into civil war, the administration provided humanitarian aid to the growing flood of refugees, pushed for sanctions and sought to organize the political opposition. The United States lagged France, Britain and Persian Gulf states in recognizing that opposition as the legitimate representative of the Syria people, but by December, Mr. Obama had taken that step.

Still, rebel fighters were clamoring for weapons and training. The White House has been reluctant to arm them for fear that it would draw the United States into the conflict and raise the risk of the weapons falling into the wrong hands. Rebel extremists affiliated with Al Qaeda had faced no such constraints in securing weapons from their backers.

When Mr. Petraeus was the commander of forces in Iraq and then-Senator Clinton was serving on the Senate Armed Services Committee and preparing for her 2008 presidential bid, she had all but called him a liar for trumpeting the military gains of the troop increase ordered by President Bush. But serving together in the Obama administration, they were allies when it came to Syria, as well as on the debate over how many troops to send to Afghanistan at the beginning of the administration.

And yet, interviews with more than a dozen current and former officials also paint a more complex picture: of a dogged diplomat and a sometimes frustrated figure who prized her role as team player, but whose instincts were often more activist than those of a White House that has kept a tight grip on foreign policy.

The disclosures about Mrs. Clinton’s behind-the-scenes role in Syria and Myanmar — one a setback, the other a success — offer a window into her time as a member of Mr. Obama’s cabinet. They may also be a guide to her thinking as she ponders a future run for the presidency with favorability ratings that are the highest of her career, even after her last months at the State Department were marred by the deadly attack on the American Mission in Benghazi, Libya.

“Secretary Clinton has dramatically changed the face of U.S. foreign policy globally for the good,” said Richard L. Armitage, deputy secretary of state during the George W. Bush administration. “But I wish she had been unleashed more by the White House.”

In an administration often faulted for its timidity abroad, “Clinton wanted to lead from the front, not from behind,” said Vali R. Nasr, a former State Department adviser on Afghanistan and Pakistan who is now the dean of the Johns Hopkins School of Advanced International Studies.