Feeling a little bamboozled by former Attorney General Jeff Sessions, congressional Republicans say they have higher hopes for successor William P. Barr and his commitment to trying to get to the bottom of how the Russia investigation began.

A year after Mr. Sessions revealed he had tapped U.S. Attorney John Huber to get to the bottom of things but with no public accomplishments since, Mr. Barr last month said it was time for a change.

He sent Mr. Huber to the showers and brought in his own man, U.S. Attorney John Durham.

The Republicans who’ve been demanding answers to the FBI’s behavior toward President Trump said the change was overdue, but were left shaking their heads over how Mr. Sessions handled things.

“I think everyone has moved on to the Bill Barr-John Durham investigation,” Rep. Jim Jordan, Ohio Republican, told The Washington Times. “The bottom line now is Bill Barr is doing a good job. Bill Barr has pledged to the get to the bottom of this.”

He and fellow Republicans say they see fishy behavior in how the FBI treated Mr. Trump both while he was a candidate, when the FBI won a secret surveillance warrant on one campaign adviser and deployed informants to try to get close to another, and again after the election, when the FBI under then-Director James B. Comey took a combative approach to the president.

An inspector general has been reviewing the FBI’s surveillance warrant, which was largely based on a now widely discredited dossier compiled by British ex-spy Christopher Steele. But Republicans had demanded more, saying a special counsel was needed to look at broader decisions about Mr. Trump, and also about decisions not to investigate more forcefully foreign donations made to the Clinton Foundation.

Answering their complaints last year, Mr. Sessions revealed he’d secretly tapped Mr. Huber, a federal prosecutor in Utah, to do a probe. Mr. Sessions said Mr. Huber could reach witnesses the inspector general couldn’t and would have the same grand jury powers as a special counsel.

Yet key witnesses said they have never spoken to Mr. Huber, and he has rebuffed lawmakers’ calls for updates on his progress.

“I look at Huber as not accomplishing any of the investigative matters that was set before him and certainly there is no briefing that came before Congress that would suggest Mr. Huber acted on what many members of Congress believed he was tasked with doing,” said Rep. Mark Meadows, North Carolina Republican.

Frustration turned to surprise last week, when Mr. Barr revealed that the man they hoped would resolve questions of anti-Trump bias at the Justice Department was sidelined the whole time.

In an interview with CBS News, the attorney general said Mr. Huber had made progress in probing decisions surrounding Hillary Clinton, but “was essentially on standby” while Justice Department Inspector General Michael E. Horowitz did his work on the FBI’s surveillance warrant against Carter Page, the Trump campaign adviser.

“So he has not been active on this front in recent months, and so Durham is taking over the role,” Mr. Barr told CBS News.

Republicans say that doesn’t jive with what Mr. Sessions had promised.

“Obviously, Attorney General Barr enjoys my 100% support and confidence and yet his interpretation of Mr. Huber’s assignment is contradicted by what was communicated to me by former Attorney General Sessions,” Mr. Meadows said.

Mr. Jordan agreed.

“News to me,” he said of Mr. Huber’s standby role. “That certainly wasn’t how it was portrayed when former Attorney General Sessions tapped him to do some investigating, but he obviously hasn’t.”

Neither the Justice Department nor a spokeswoman for Mr. Sessions returned requests for comment.

Howard Krongard, a State Department inspector general under President George W. Bush, said it is “a little unusual” for a government watchdog such as Mr. Horowitz to have a U.S. attorney put on standby. He said he typically referred cases to the appropriate district, usually the Eastern District of Virginia, for prosecution.

“I didn’t need a standby,” he said. “I’m not sure what Michael would have [been working on], but I’m not sure he would need a standby.”

The congressmen said they aren’t sure why there is a discrepancy in the way the two attorneys general described Mr. Huber’s role, but they are ready to move on.

“I think Huber didn’t investigate anything that he was tasked with investigating, and I am going to count on the new sheriff in town,” Mr. Meadows told The Times.