[2] Galán made his senior debut on 15 September 2013, playing the last 30 minutes in a 1–0 home win against CD Solana for the Regional Preferente championship.
Galán made his professional debut on 12 October 2016, starting as a left back in a 2–1 Copa del Rey away win against Cádiz CF.
[9] Galán was an undisputed starter during the 2017–18 campaign; converted to a left back by manager Jorge Romero,[10] he went on to score two goals in 40 appearances as his side narrowly avoided relegation.
On 31 July 2021, after suffering another relegation with Huesca, Galán signed a five-year contract with Celta de Vigo in the top tier.
[14] On 24 January 2024, Atlético Madrid sent Galán on loan to fellow La Liga club Real Sociedad until the end of the 2023–24 season.