Shortly after the Federal Reserve convened its last meeting, President Trump took to social media to mount a familiar line of attack. He demanded lower interest rates, and lashed out at Jerome H. Powell, then the chair of the central bank — even sharing an edited image Mr. Powell hurtling into a dumpster filled with trash.

Mr. Trump’s unrelenting pressure had little effect on the Fed, which has kept borrowing costs unchanged for months as it tried to tame the fallout from the U.S. war with Iran. For Mr. Powell, it was the final major act in a tumultuous term in leadership — and for his replacement, Kevin M. Warsh, it offered a sign of the challenges still to come.

As the president’s long-awaited, handpicked Fed chairman, Mr. Warsh must navigate the economic headwinds — and the many political risks — that come with serving in Mr. Trump’s second term. Like his predecessor, Mr. Warsh is bound to face the unyielding attention of the man who nominated him, and could similarly find himself on the receiving end of fierce and public pressure to lower rates.

In some ways, the task for Mr. Warsh is laid bare by the unusual circumstances in which he inherited the job.

Mr. Trump nominated Mr. Warsh back in January, amid months of unusually aggressive White House attacks on the Fed and its members. The president openly courted a roster of loyalists at the central bank, and he repeatedly flirted in public with the idea of firing Mr. Powell, despite having elevated him to the job during his first term.

At political rallies and on social media, Mr. Trump savaged Mr. Powell, while the president’s deputies investigated the Fed chair, an inquiry that a judge would later find to be politically motivated. And Mr. Powell was not alone: Mr. Trump also tried to oust another Fed member, Lisa D. Cook, in a case that would eventually reach the Supreme Court. (The justices could render a verdict in that case as soon as this week.)

The meddling often spooked markets, angered lawmakers from both parties and cast a shadow of doubt over Mr. Warsh before he could even take the job at the Fed, where he previously served as a governor. It forced Mr. Warsh to face uncomfortable questions from Congress about his ability to resist Mr. Trump’s demands.

At a tense confirmation hearing in April, Mr. Warsh repeatedly tried to convince lawmakers that Mr. Trump had “never asked me to predetermine, commit, fix, decide on any interest rate decision in any of our discussions, nor would I ever agree to do so.” Many Democrats remained unconvinced, and later opposed Mr. Warsh’s confirmation, which the Senate delivered in May.

That largely party-line vote afforded Mr. Trump his long-sought, new Fed leader precisely at a moment when the central bank seemed least inclined to deliver on his demands for lower interest rates. In fact, Mr. Warsh’s first meeting, which began Tuesday, came as economists continued to debate the odds of a rate hike, with prices now rising at their fastest clip in over three years.

Mr. Warsh is set to announce the Fed’s next rate decision on Wednesday in the same setting that frequently compelled Mr. Trump’s to issue his fiercest public criticisms against Mr. Powell.

The president, for his part, has hinted in recent weeks that he may dial back some of the pressure on his newly confirmed chair. At a swearing-in ceremony for Mr. Warsh last month, the president said he wanted his new Fed chair to be “totally independent” when it came to setting interest rates.

“Don’t look at me,” Mr. Trump said. “Don’t look at anybody. Just do your own thing and do a great job.”