[7] Before the start of the 2013 season, Gott had recovered from a minor bout of bursitis and he was on the preseason watch list for the NCBWA Stopper of the Year Award.

[9][10] In early 2013, Baseball America named Gott as the second-best draft prospect from the University of Kentucky behind Corey Littrell.

[13][14][15] After making four appearances with Eugene in which he pitched to an earned run average (ERA) of 2.08, walked three, and struck out eight in 4+1⁄3 innings with no decisions,[15] he was promoted to the Fort Wayne TinCaps of the Single–A Midwest League.

[21] He made eight appearances for the Solar Sox with no decisions, posting an ERA of 6.14 in 7+1⁄3 innings of work, walking two, striking out four, and recording one save.

[15][22] Gott started the 2015 season with Arkansas, pitching 19+2⁄3 innings in 18 appearances with a record of 1–0 and an ERA of 3.20, striking out 20, walking seven, and going 8-for-8 in save opportunities.

[15] Promoted to the Salt Lake Bees of the Triple–A Pacific Coast League on May 24,[15] he blew his only save opportunity but gave up no earned runs in seven appearances for the Bees, striking out 10 and walking five in 8+1⁄3 innings of work with no decisions,[15] giving him overall minor-league statistics for 2015 of 28 innings pitched in 25 games with a record of 1–0, an ERA of 2.25, 30 strikeouts, 12 walks, and eight saves in nine opportunities.

[citation needed] Later in the season, he became an important part of the Angels' bullpen after closer Huston Street and pitcher Joe Smith both suffered injuries.

[citation needed] He finished the season with the Angels, appearing in 48 games for them, going 0-for-4 in save opportunities but striking out 27, walking 16, and posting a record of 4–2 and an ERA of 3.02 in 47+2⁄3 innings pitched.

[15] Gott took the loss in his only appearance for the Gulf Coast League Nationals, giving up two earned runs and striking out two in two innings pitched.

[15] On July 27, he reported to the Auburn Doubledays of the Low–A New York-Penn League to continue his rehabilitation assignment and made one appearance for them, giving up an earned run and striking out two in two innings of work.

[26] The Nationals recalled Gott on July 14 after they optioned Sammy Solis to the minors and placed Joe Ross on the disabled list with a torn ulnar collateral ligament of the elbow.

[15] After a standout performance in spring training in which he posted a 1.54 ERA in 11+2⁄3 innings over 11 appearances,[29] Gott began the 2018 season on the Nationals′ 25-man roster.

To start the season, he appeared in five games, pitching five innings and giving up three earned runs for a 5.40 ERA before he was optioned to Syracuse on April 16.

[15] Gott had a 5.28 ERA, an 0–2 record, seven walks, and 12 strikeouts in 15+1⁄3 innings over 17 major-league appearances on the season[34] when the Nationals optioned him to Syracuse again to make room on their roster when they activated reliever Ryan Madson from the disabled list.

[32] The Nationals again recalled Gott from Syracuse, along with reliever Wander Suero, on June 11 when they placed starting pitcher Stephen Strasburg and reliever Brandon Kintzler on the disabled list,[32] and on June 13[32] – by which time he had lowered his major-league ERA for the season to 4.96 but had given up eight walks along with striking out 12 in the majors for the year[35] – again optioned him to Syracuse when they called up starting pitcher Erick Fedde from the Chiefs.

[37] Gott made 15 appearances for the Giants in 2020, pitching to a ghastly 10.03 ERA with 8 strikeouts and 13 earned runs over 11.2 innings of work.

[51] On March 22, 2024, it was announced that Gott would require Tommy John surgery to repair a fully torn UCL, ending his season.