In 2006, Vene moved to Lithuania and joined Žalgiris' junior team Žalgiris-Arvydas Sabonis school.

With Žalgiris, Vene won the Nike International Junior Tournament in 2007 and the Nacionalinė krepšinio lyga (NKL) in 2008.

In the 2014–15 season, Vene averaged 3.4 points, 1.2 rebounds and 0.5 assists per game in the Euroleague and won his second Lithuanian Championship, after Žalgiris defeated league rivals Lietuvos rytas 4–0 in the finals.

[7] On 29 September, he was sidelined for three months due to a leg injury and didn't play any games for Reggiana.

[9] On September 5, 2018, Vene signed a six-week deal with Manresa of the Liga ACB as a replacement for the injured Justin Doellman.

[17] While on the team, Vene played a significant role particularly in a number of clutch wins, including over Maccabi Tel Aviv, and over Lenovo Tenerife in the semi-finals of the Basketball Champions League Final Four.

Vene was a member of the Estonian national under-18 basketball team that competed at the 2007 FIBA Europe Under-18 Championship and finished the tournament in 12th place.

As a member of the senior Estonian national team, Vene competed at the EuroBasket 2015, averaging 10 points, 6.4 rebounds and 1.6 assists per game.

Vene was named the captain of the Estonian national team in 2020 ahead of the EuroBasket 2021 qualification games.