2009-10: Kristers Gudlevskis made his pro hockey debut as a 17-year-old in his native Latvia —appearing in nine games for HK Ogre — and played for the Ozolnieki/Juniors in the Belarus second league. Gudlevskis was 1-4 with a 5.13 goals against and .856 save percentage in five games for Latvia at the 2010 U18 World Junior Championship. He stopped 33 of 37 shots in Latvia's only win, a shootout victory over Belarus in the relegation round. Gudlevskis was selected by Dinamo Riga in the seventh round (147th overall) of the 2010 KHL Draft.
2010-11: Gudlevskis appeared in 49 games for HK Riga in Russia's U22 Minor Hockey League league and represented Latvia in the 2011 U20 Division 1A World Junior Championship. Gudlevskis was 26-16-2 with 7 shutouts and had a 2.20 goals against and .920 save percentage for HC Riga. In three playoff games he was 0-3 with one loss coming in overtime and had a 4.16 goals against and .862 save percentage. Gudlevskis was 1-0 for Latvia at the D1A WJC as a backup to Janis Kalnins – stopping 16 of 17 shots in his only game. Latvia finished first in the tournament to gain elevation to the main pool for 2012.
2011-12: Gudlevskis returned to HK Riga for his second season and again represented Latvia at the U20 level; handling the bulk of the goaltending in the 2012 World Junior Championship. He was 16-16-5 for HK Riga, appearing in 40 games, and had 1 shutout with a 2.39 goals against and .918 save percentage. In four playoff games he was 1-3 with a 3.50 goals against and .896 save percentage. Gudlevskis was 1-4 with a 5.15 goals against and .865 save percentage in five games at the WJC, stopping 22 of 23 shots in Latvia's 2-1 overtime win over Denmark to avoid relegation.
2012-13: Gudlevskis made his KHL debut, appearing in two games for Dinamo Riga, and played for Latvia in the 2013 IIHF World Championship after appearing in 59 MHL games for HK Riga. He was 1-1, stopping 35 of 38 shots in his brief time with Dinamo, finishing with a 2.18 goals against and .921 save percentage. Sharing the goaltending for Latvia with veteran Edgars Masalskis at the WC, he was 2-2 with a 2.22 goals against and .925 save percentage. Gudlevskis was 27-18-11 with 3 shutouts in 56 regular season games for HK Riga and had a 2.09 goals against and .927 save percentage. In three playoff games he was 0-3 and had a 7.42 goals against and .747 save percentage. Not among the ten Europe goalies in Central Scouting's final rankings, Gudlevskis was drafted as a 20-year-old by Tampa Bay in the fifth round (124th overall) of the 2013 NHL Draft.