He spent his early professional career in Spain, playing six La Liga games for Levante and 99 in Segunda División for Reus and Tenerife.

[5] Moore made his senior debut for the club on August 22, 2015, coming on as a second-half substitute for Javi Soria in a 1–1 Segunda División B home draw against CD Atlético Baleares.

[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.

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.

[17] Moore played 101 total games for the team from the Canary Islands,[18] scoring once to open a 4–2 win at Extremadura UD on February 8, 2020.

[20] On July 19, 2022, Moore signed with Major League Soccer side Nashville SC for a reported fee of US$2 million.

[29] 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.