[6] In 2010, Mesa signed with another reserve team, Las Palmas Atlético in the fourth level, being promoted to the main squad the following year.
[7] On 8 October 2011 he appeared in his first game as a professional, starting in a 2–1 away win against Celta de Vigo in the Segunda División.
[8] Mesa finished the campaign with 22 appearances (ten starts, 947 minutes of action) and, on 31 August of the following year, he was loaned to Atlético Baleares of the third division.
[14] On 6 July 2017, Mesa signed a four-year deal with Premier League team Swansea City for a fee of £11 million.
[17] In June, the move was made permanent for three years,[18] and he scored two goals in 31 matches during the season as the club finished in sixth place.