Born on 13 December 1965 in Madrid, Cospedal was however chiefly raised in Albacete, studying in the later city's Colegio La Anunciata de Nuestra Señora del Rosario and in the Sabuco High School. She moved to Madrid to go to college and, after earning a licentiate degree in Law at the CEU San Pablo University, she passed the competitive public examinations to join the State Lawyers Corps in 1991, serving in this body of top civil servants until 1996. Cospedal married aristocrat José Félix Valdivieso-González y Bravo de la Laguna in 1995; the marriage ended three years later, in 1998, when it was nullified by the Church. At a certain point she started calling herself "de Cospedal" in public which sounded more aristocratic but more recently she reverted to plain "Cospedal". She affiliated to the People's Party in 1999. Following the 2000 general election, she was appointed to the post of Under-Secretary of State for Public Administrations and Territorial Policy. After roughly 2 years in office, she was appointed Secretary of State of Security in the Ministry of the Interior, then led by Ángel Acebes. In December 2004, Esperanza Aguirre the president of the Madrid region, appointed Cospedal as the new minister for Transports and Infrastructures in the Regional Government of the Community of Madrid in replacement of Francisco Granados.
Regional president of Castilla–La Mancha
She was chosen as the People's Party candidate to the presidency of the autonomous community of Castile-La Mancha vis-à-vis the 2011 regional election. The PP list commanded a qualified majority of seats in the election, with the outcome of the investiture the first PP president in the region, after 28 years of PSOE governments. With Cospedal repeating as prospective PP candidate for the regional premiership in the context of the 2015 regional election, the PP, despite winning the most votes at the election, failed to attain an absolute majority of seats and PSOE's Emiliano García-Page became President of Castile-La Mancha following an investiture agreement with Podemos.
After the announcement of Mariano Rajoy stating his resignation to party leadership, Cospedal contested as candidate to the July 2018 party vote among affiliates to determine the new party leader. Her opponents were former Deputy PM and staunch rival Soraya Sáenz de Santamaría, PP's Vice-Secretary for Communication Pablo Casado, former foreign ministerJosé Manuel García-Margallo, MP José Ramón García-Hernández and grassroot member Elio Cabanes. Cospedal was left out of the race as she commanded the 3rd position in number of votes in the primary election after Sáenz de Santamaría and Casado. Shortly before the runoff among party delegates between Casado and Sáenz de Santamaría, Cospedal publicly declared that she thought that "Pablo Casado could be magnificent option ".
Secondary role in the PP
Following her exit from the cabinet she also served as Chairwoman of the Committee on Foreign Affairs of the Congress of Deputies from 13 September 2018 to 14 November 2018, when she resigned to her seat.
Following her abrupt exit from politics after the "Villarejo Scandal", Cospedal asked for re-incorporation to her career as State Lawyer on 3 January 2019, and soon after she started to work for the Chamber for Contentious Administrative proceedings of the Supreme Court, also reportedly assuming later some additional work in the Chamber of Military proceedings of the Supreme Court. On 24 March 2020 it was reported that she tested positive for COVID-19 during COVID-19 pandemic in Spain, together with her husband, but not in a serious condition.
