In 2010, Atlético Cirbonero finished in the third position of the Group 14 of Tercera División and qualified for the first time to the promotion playoffs to Segunda División B, but was eliminated in the first round by Ayamonte CF.
Six years later, the club qualified again to the promotion playoffs, this time as runner-up of the Navarrese group, but it did not pass from the first round, where was beaten by CD Cayón.
In 2016, Atlético Cirbonero made its debut in the Copa del Rey. Despite being a Tercera División team, it beat SD Ponferradina and Racing de Ferrol, both Segunda División B, after the penalty shootout. In the 2018-19 season the club finished 7th in the group 15 of the Tercera División.