The biggest untapped onshore trove of oil in North America is believed to lie beneath the refuge’s coastal plain along the Beaufort Sea. For more than a generation, opposition to drilling has left the refuge largely unscathed, but now the Trump administration, working with Republicans in Congress and an influential and wealthy Alaska Native corporation, is clearing the way for oil exploration along the coast.

The E.P.A. chief, who has reversed Obama-era rules on coal mining, enjoyed a superfan experience at a University of Kentucky basketball game — courtesy of an industry executive. But there was more to the game last December than a superfan experience for Mr. Pruitt and his son, who joined him. They sat in seats belonging to Joseph W. Craft III, a billionaire coal executive who has engaged in an aggressive campaign to reverse the Obama administration’s environmental crackdown on the coal industry. Mr. Craft and his wife donated more than $2 million to support President Trump’s candidacy and inauguration.