On 13 December 2011, Gálvez made his debut with Sporting's main squad in a Copa del Rey match against RCD Mallorca (1–0 away win, 2–1 aggregate loss).
[5] The following 15 January, again as a starter and a stopper, he made his first La Liga appearance for the Asturians, scoring the first goal of the game in an eventual 2–1 home victory over Málaga CF.
[9] On 13 May 2014, after consecutively helping Rayo retain their top-flight status, free agent Gálvez signed a three-year contract with SV Werder Bremen in Germany.
[10] For most of the first half of his first season he was deployed in defensive midfield by coach Robin Dutt, but under the former's successor Viktor Skrypnyk he became a constant in the centre of defence, until injuries limited him to five appearances from January to May 2015.
[11] Continuing injury problems over the summer break proved detrimental to pre-season training for Gálvez, as he was mostly used as a backup for Assani Lukimya at the beginning of the 2015–16 campaign.