Struna found more playing time at the beginning of the 2009–10 season, appearing in fifteen league games and twice in the Slovenian Cup.
He made his first appearance of the season on 13 July 2010, making his European debut by coming on as a substitute in a UEFA Champions League qualifying match against Dinamo Zagreb.
[8] Struna made his first appearance of the 2011–12 season in a UEFA Europa League qualifying match on 30 June 2011, a 1–1 draw with Shakhter Karagandy.
He scored his only goal of the season on 14 September 2011 in a 2–0 win over Olimpija Ljubljana in a Slovenian Cup match.
[9] In the summer he went on loan to Varese of Serie B, with an option for his new club to acquire 50% of his transfer rights by the end of the season.
In part due to their stingy defense, Carpi finished first in the league and won promotion to Serie A for the first time in club history.
Struna made 35 Serie B appearances to help Palermo end the year with the second best defense, allowing only 39 goals in 42 matches, and finish in fourth place, qualifying for the promotion playoffs.
[23] With his contract set to expire at the end of the season and the club in a poor financial situation, Palermo agreed to sell Struna in the January transfer window.
[8] He missed the MLS season opener and the first leg of the quarterfinals tie with Tigres UANL due to a slight thigh injury.
[26] Struna returned to action on 9 March 2019, making his MLS debut in a 2–1 win over the Montreal Impact.
[27] Despite Struna's strong performances, Houston ended the season in tenth place in the Western Conference, missing out on the MLS Cup Playoffs.
[31][32] For the final five games of the season, head coach Tab Ramos opted to bench Struna.
[33] He made his Montréal debut on 17 April, coming on as a substitute in a 4–2 win over Canadian Classique rivals Toronto FC.
[35] On 3 November 2022, Struna signed with Italian second-tier Serie B club Perugia until the end of the 2022–23 season, with an option to extend.
[39] Struna made his competitive debut for Slovenia on 8 October 2016 in a 2018 FIFA World Cup qualifier, getting the start in a 1–0 win over Slovakia.
[41] He is a big fan of basketball, particularly Michael Jordan and fellow Slovenians Goran Dragić and Luka Dončić.
[26] Struna says that he likes basketball more than football and would stay up to 4 am watching NBA games while living in Italy.