In 1989 Delgado entered the Spanish Prosecutor Service, she was first assigned as a prosecutor at the High Court of Justice of Catalonia. Later she was assigned to the Special Anti-Drug Prosecutor's office. From 1993 Delgado was a prosecutor at the Audiencia Nacional. In that capacity, she led the prosecution on several high-profile drug and terrorist cases, as promoted several Universal jurisdiction cases tried at the court. After the 2004 Madrid train bombings she specialised in Islamic terrorism. For a short period of time Delgado was the spokeswoman of the Prosecutor General's office. In 2011 she was a support prosecutor at the International Criminal Court. As a prosecutor she has shown herself as favourable to universal jurisdiction and very vocal on corruption issues. In 2013 she opposed the extradition of Hervé Falciani to Switzerland considering him a valuable asset in fight against tax fraud and corruption.
After Mariano Rajoy received a vote of no confidence, Prime Minister Pedro Sánchez appointed Delgado as Minister of Justice in June 2018. As Minister of Justice she also holds the honorary position of First Notary of the Kingdom. Thus, on 7 June she took office as Minister before the King at Palace of Zarzuela. During her time in office she had a difficult relationship with the opposition. Proof of this is that Parliament requested her resignation three times. On September 2018, the Senate requested her resignation for 149 votes in favour, 82 against and 7 abstentions. The reason, according to the opposition, was that the minister did not sufficiently defend the Supreme Court Justice, Pablo Llarena, before the Belgian courts. On October 9, 2018, the Congress of Deputies requested her resignation for 166 votes in favour, 91 against and 83 abstentions. The motion, at People's Party initiative, considered that Delgado should not continue in the office because of her "perverse friendships" with the retired police commissioner José Manuel Villarejo and the former National Court justice Baltasar Garzón. A month later, on November 22, 2018, the Congress of Deputies requested her resignation again for urging the State Lawyers Corps to rule out the crime of rebellion to jailed Catalan separatist leaders. On October 24, 2019, she was one of the representatives of the caretaker government in the exhumation of Francisco Franco, serving as First Notary of the Kingdom, attesting to the incidentless extraction of the coffin with the remains of the dictator. She left the office of Minister of Justice on January 13, 2020, being replaced by the socialist Juan Carlos Campo.
