Born in Barcelona, Catalonia, Gallego had several working-class jobs alongside his amateur footballing career, such as lorry driver, builder and air conditioning installer.

[12] Gallego made his debut as a full-time professional at the age of 31 years and 11 months on 24 August 2018, starting the 0–1 home loss against Deportivo de La Coruña.

[17] On 16 January 2019, Gallego signed a two-and-a-half-year deal with La Liga strugglers SD Huesca, for a rumoured fee of €2 million.

[22] Gallego's maiden appearance in the UEFA Europa League occurred on 19 September 2019, as he started the 1–0 home win against Trabzonspor in the group stage.

[23] On 28 January 2020, after being rarely used,[24] Gallego was loaned to fellow top-flight CA Osasuna with an obligatory buyout clause if the team avoid relegation.