The Rangers selected Trevino in the sixth round of the 2014 MLB draft out of Oral Roberts University.

Trevino attended St. John Paul II High School in Corpus Christi, Texas.

Trevino played for the Hickory Crawdads of the Single–A South Atlantic League in 2015, hitting .262/.291/.415/.707 with 14 home runs along with 63 RBIs, while becoming a full-time catcher.

[9] Trevino spent 2017 with the Frisco RoughRiders of the Double-A Texas League, hitting .241/.275/.323/.598 with 7 home runs and 42 RBIs.

Trevino played in 24 games for the Rangers in the pandemic shortened season in 2020, slashing .250/.280/.434 with two home runs and nine RBIs in 76 at-bats.

[19] On April 2, 2022, the Rangers traded Trevino to the New York Yankees in exchange for Albert Abreu and Robert Ahlstrom.

[20] He supplanted Kyle Higashioka as the Yankees starting catcher and was named an American League All-Star reserve.

On July 21, it was announced that Trevino would undergo season–ending surgery to repair a ligament tear in his right wrist, which had bothered him since spring training.

[29] On December 20, 2024, the Yankees traded Trevino to the Cincinnati Reds in exchange for Fernando Cruz and Alex Jackson.