In August 2014, Moore moved to Spain and went on to train with three teams in the city of Valencia: Valencia CF, Levante UD, and Huracán Valencia CF,[4] being assigned to the latter's Juvenil A squad, as the club waited for an international transfer certificate. On May 9, 2015, he finally signed a contract with Huracán.[5]
The following year, he was included in a first-team matchday for the first time on September 30, 2017, for a La Liga match against Deportivo Alavés.[9]
Moore made his main squad debut on October 26, 2017, starting in a 2–0 away win against Girona FC for the season's Copa del Rey.[10] Three days later he made his La Liga debut, replacing Ivi in a 2–2 draw at SD Eibar.[11]
Following success in the previous two fixtures, Moore started his first game for Levante on November 18, 2017, in a 2–0 away defeat of UD Las Palmas.[12] He became only the fourth American to play in La Liga after Kasey Keller, Jozy Altidore, and Oguchi Onyewu.[13] He finished the campaign with eight first-team appearances.
On July 13, 2018, Moore agreed to a season-long loan deal with Segunda División side CF Reus Deportiu,[14] but on December 28, he was one of five players who left the team due to unpaid wages.[15]
Tenerife
On July 24, 2019, Moore signed a three-year contract with CD Tenerife also in the second division.[16] The following May, his deal was extended until 2024.[17]
On July 19, 2022, Moore signed with Major League Soccer side Nashville SC for a reported fee of US$2 million.[21] He made his debut 11 days later in a 1–1 home draw with Vancouver Whitecaps FC, playing for 63 minutes.[22]
Moore received his first senior team call-up for a friendly against Paraguay on March 18, 2018.[25] He made his full international debut on June 2, as a 70th-minute substitute for DeAndre Yedlin in a 1–2 friendly loss away to the Republic of Ireland.[26]
Uncapped since November 2018, Moore was called up by coach Gregg Berhalter for the 2021 CONCACAF Gold Cup.[27] On July 18 in the final group game against Canada, he scored his first international goal and the only one of the American win; it came after 20 seconds, breaking Clint Dempsey's all-time record for the team's fastest goal by 14 seconds.[28] He played all of his team's games as they won the title, though his appearance in the final against Mexico was off the bench as Reggie Cannon had recovered from injury.[29][30]
On November 9, 2022, Moore was named by Berhalter to the final U.S. squad for the 2022 FIFA World Cup.[31]