“I want to make this clear: Obama was a great president,” Mr. Brien said. But his energy policies, he said, “would have devastated the tribe.”

In November, Big Horn County, which contains most of the reservation, cast 1,833 votes for Mr. Trump and 2,061 for Hillary Clinton, going significantly more Republican than it had in recent years. “Under Trump,” Mr. Brien added, “the door is opening.”

In 2013, the tribe made a deal with Cloud Peak Energy for a second coal mine, the Big Metal, which could bring $10 million to the Crow in the project’s first five years. Cloud Peak hoped to export that coal to Asia through a proposed terminal in Washington State. That terminal was vetoed by the Army Corps of Engineers under Mr. Obama, but Crow leaders hope to reopen the discussion.

One of the first tests of Mr. Trump’s commitment to coal could come in his administration’s response to the Navajo and Hopi, who derive millions of dollars from a coal-fired power plant nestled amid red rocks in Arizona, as well as an associated mine.

In February, operators of the plant, called the Navajo Generating Station, voted to shut it down at the end of 2019, 25 years ahead of schedule. The move could leave 1,885 people without work, counting associated jobs, said a Navajo spokesman, Mihio Manus.

“We’re in chaos over this whole plant closure,” said the Navajo president, Russell Begaye, who is asking the federal government to take majority ownership of the plant and keep it running as the tribe develops other revenue. The federal government is one of several current owners.