During the Trump administration, Mr. Fletcher was a professor at Stanford Law School, where he helped direct a Supreme Court clinic. When he joined, his co-director, the prominent law professor Pamela S. Karlan, praised him as versatile.

“Baseball scouts talk about five-tool players, and Brian is the paradigmatic five-tool Supreme Court lawyer,” she said. “He writes powerfully and quickly, has great judgment, gives the students exactly the right combination of guidance and ownership, and is wonderfully supportive of his colleagues and staff as well.”