[5] He trained in his hometown of Brno with coach Petr Starec and in Oberstdorf, Germany with Karel Fajfr.

[12] He returned in time for the 2009 Europeans, where he finished tenth, and then set a new personal best at the 2009 Junior Worlds to win the silver medal behind Adam Rippon.

Březina debuted on the senior Grand Prix circuit, finishing fourth at the 2009 Skate Canada International.

He won the bronze medal at 2009 NHK Trophy and defeated Tomáš Verner to win the Czech Championship.

Březina was forced to withdraw from the 2010 Cup of China after undergoing surgery for a varicose vein in his abdomen.

Skaters who had placed in the top six at the 2011 Worlds were given a newly introduced option of competing at three Grand Prix events.

[17] Březina elected to do so and was assigned to 2011 Skate America, 2011 Trophée Eric Bompard, and 2011 Cup of Russia.

At the 2012 World Championships, Březina picked up a small silver medal for the short program and finished sixth overall after the free skate.

[21] Březina finished sixth at 2012 Skate America and won the bronze medal at the 2012 Rostelecom Cup.

He withdrew after the short program on 26 March, having pulled ligaments in his right ankle on the triple flip take-off.

[25] Due to the high cost of training in the United States,[25] he decided in June 2014 to rejoin Karel Fajfr in Oberstdorf.

Following a sixth-place finish at Nebelhorn, Brezina placed eighth and seventh at these two Grand Prix assignments, Skate Canada International and the NHK Trophy.

[29] He finished eighteenth at the event in Finland, earning a spot for the Czech Republic at the 2018 Winter Olympics.

Beginning with two events on the Challenger Series, Březina placed ninth at the U.S. International Classic and sixth at the Finlandia Trophy.

Following an eighth-place finish at Europeans, Březina competed at his third Olympic Games in Pyeongchang, South Korea.

The season concluded at the 2018 World Championships in Milan, Italy, where he placed tenth, setting a new personal best in the free skate.

[31] Březina placed fourth at the Final, finishing 8.23 points behind Cha Jun-hwan after doubling a jump in his short program and falling on a quad Salchow in the free skate.

[35] Březina opted not to begin his season with a Challenger event, instead competing at the 2019 Shanghai Trophy, where he placed fourth.

Competing at the 2020 European Championships, Březina placed first in the short program despite performing only a quad-double in his combination jump, winning a gold small medal.

[44] Following the results of the 2021 CS Nebelhorn Trophy, he was announced as part of the Czech Olympic team, this time alongside his sister Eliška.