After his junior year, Povse was drafted by the Atlanta Braves in the third round of the 2014 Major League Baseball draft.[3][4] He signed with the Braves and made his professional debut with the rookie-level Danville Braves.[5] In an August start against the Burlington Royals, Povse did not allow a hit until the seventh inning, sending Danville to a 10–1 win.[6] He finished 2014 with a 4-2 record and a 3.42 ERA in 12 games (11 starts) for Danville. Povse spent 2015 with both the Single-A Rome Braves and High-A Carolina Mudcats, posting a combined 5-5 record and 4.15 ERA in 17 starts, and started 2016 with Carolina.[1][7] He was later promoted to the Double-A Mississippi Braves. Povse finished 2016 with a combined 9-6 record and 3.36 ERA in 26 starts.[2]
Seattle Mariners
On November 28, 2016, Povse and Rob Whalen were traded to the Seattle Mariners organization in exchange for Alex Jackson and Tyler Pike.[8][9] Povse started 2017 with the Double-A Arkansas Travelers and was called up to the Mariners on June 18.[10] He made his MLB debut on June 22, allowing 3 runs in two-thirds of an inning. He finished his rookie season with a 7.36 ERA in 3 major league appearances. He spent the 2018 season in the minor leagues, posting a 5-9 record and 5.46 ERA in 18 games between Arkansas and the Triple-A Tacoma Rainiers.
Povse was designated for assignment on January 27, 2019, following the signing of Hunter Strickland.[11] He cleared waivers and was sent outright to Triple–A Tacoma on February 1.[12] He did not make an appearance for the organization on the season and was released by the Mariners on December 19.[13]
On February 20, 2022, Povse signed with the Wild Health Genomes of the Atlantic League of Professional Baseball.[15] Povse made 25 starts for the Genomes in 2022, recording a 6-10 record and 5.98 ERA with 129 strikeouts in 129.1 innings pitched. He became a free agent after the season.