The governor of Kansas, Sam Brownback, is expected to be nominated as the United States ambassador at large for international religious freedom. If Mr. Brownback is confirmed, as expected, the state’s lieutenant governor, Jeff Colyer, will step in to lead the state.

Mr. Colyer, who like Mr. Brownback is a Republican, would inherit a state that has struggled with budget shortfalls and a party that has been split by philosophical debates about taxation.

It is not known when the Senate might take up Mr. Brownback’s planned nomination, which President Trump announced on Wednesday.

A Conservative

First elected to the Kansas House of Representatives in 2006, and to the State Senate two years later, Mr. Colyer is a political conservative aligned with Mr. Brownback on most issues.

“I don’t expect much different with the new governor,” said State Representative Jim Ward, the Democratic leader in the House. “Jeff Colyer has walked in lock step with Sam Brownback for the last six-and-a-half years.”

Despite spending more than a decade in state government and more than six years as lieutenant governor, Mr. Colyer has largely avoided the political spotlight. Though ideologically similar to Mr. Brownback, some expect him to take a more hands-on tack in partnering with lawmakers and brokering compromise.

“He has that working relationship, being a former state senator, with the Legislature,” said Kelly Arnold, the chairman of the Kansas Republican Party. “He will have a different leadership style.”

A Doctor

Mr. Colyer, a married father of three, is a plastic surgeon with a practice in suburban Kansas City, where he lives. He has taken several trips overseas as a volunteer surgeon in combat zones, including work in Afghanistan and Iraq, and in Rwanda during that country’s genocide.

Mr. Colyer took the lead in designing KanCare, the state’s privatized Medicaid program. The program has been challenged in large part because of funding issues that have left many providers without reimbursements, but Mr. Colyer has framed it as a success that saved taxpayer money and expanded services.

“It’s not a perfect system,” said State Senator Carolyn McGinn, a Republican. “Now that he’ll be in a big leadership role, I hope that he wants to perfect it.”

Cleared by a Grand Jury

Mr. Colyer and others in the Brownback administration were investigated and cleared by a federal grand jury as part of an inquiry into loans made in 2013 and 2014 to the governor’s re-election campaign.

He had made three loans worth $1.5 million during that period, and political opponents theorized that they were structured to inflate fund-raising success. Mr. Colyer and Mr. Brownback strongly denied any wrongdoing, and no charges were ever filed.

A State in Turmoil

Mr. Colyer would ascend to the governorship after a turbulent legislative session and amid uncertainty about the legality of the state’s school funding mechanism, which the Kansas Supreme Court could rule on at any time.

Lawmakers, including many Republicans, bucked Mr. Brownback on his signature tax-cutting policies this year, passing a bill to raise taxes and then overriding his veto. Some Republicans also dissented and tried to enact Medicaid expansion, but Mr. Brownback’s veto on that measure was sustained.

State agencies have cut their services in recent years after tax revenue collections repeatedly failed to meet projections.

A Deep-Rooted Kansan

Mr. Colyer, a fifth-generation Kansan, graduated from a Roman Catholic high school in Hays, in the western part of the state. He studied at Georgetown and Cambridge, then returned to Kansas to attend medical school.

Jim McNiece, a Republican member of the state Board of Education, said that he taught Mr. Colyer in high school in the 1970s, recalling him as “very articulate and very competitive.”

The two men reconnected decades later when they were both in politics, and Mr. McNiece took the lieutenant governor to tour schools and discuss education issues. They have also met with students to promote a citizenship award that Mr. Colyer started to recognize community service.

“I think he’s approaching it by using the visits that we have to learn more about the public schools in Kansas,” Mr. McNiece said earlier this year. “I give him high marks for being willing.”

A Looming Election

Mr. Brownback’s term is set to expire in January 2019, and a wide field of Republicans and Democrats have already lined up for next year’s election.

Mr. Colyer has not declared his candidacy, but had been widely rumored as a likely candidate regardless of whether Mr. Brownback served out the remainder of his term.

If he seeks a full term, Mr. Colyer would face several well-known opponents in the Republican primary, including Kris Kobach, the Kansas secretary of state, who has gained national attention for his unproven claims about voter fraud.

“He’s a good guy,” Mr. Kobach said of the lieutenant governor. “I don’t think it fundamentally changes the dynamic of the 2018 race regardless.”