Wier started his legal career serving as a law clerk to Judge Eugene Edward Siler Jr. of the United States Court of Appeals for the Sixth Circuit.

Prior to his judicial service, he worked in private practice as a member of the law firm Ransdell & Wier PLLC and, before that, as an associate with the Lexington, Kentucky, law firm Stoll, Keenon & Park.

[2] Wier's service as a magistrate terminated when he was elevated to district court judge.

[3] On August 3, 2017, President Donald Trump nominated Wier to serve as a United States District Judge of the United States District Court for the Eastern District of Kentucky, to the seat vacated by Judge Amul Thapar, who was elevated to the United States Court of Appeals for the Sixth Circuit on May 25, 2017.

[6] On June 4, 2018, the United States Senate invoked cloture on his nomination by a 90–1 vote.