SYDNEY, Australia — President Trump this week nominated a Republican lawyer to become the United States ambassador to Australia, filling the long vacant post with a Washington insider who helped the president select his 2016 running mate.

The lawyer, Arthur B. Culvahouse Jr., who is expected to be confirmed by the Senate, will be the first American ambassador to Australia in two years.

The delay in selecting an ambassador has been a sore point between the two countries, with one former prime minister saying the snub indicated Australia had become a “second-class ally.”

Mr. Culvahouse’s nomination represents an effort to repair the relationship at a time when Australia is looking to the United States to help balance an emboldened China in the Asia-Pacific region.