Cooke obtained a pharmacy degree at Trinity College, Dublin, Ireland in 1982, following which she remained at Trinity to complete Masters degrees in Science and in Business Administration [3]

Starting in 1985, she held various positions in the pharmaceutical industry and from 1991 to 1998 she was a board member of the European Federation of Pharmaceutical Industries and Associations (EFPIA), a lobbying organisation of the largest European pharmaceutical companies.[4][5] There she spent eight years lobbying for the "Big 30" of the European pharmaceutical industry, including Pfizer, AstraZeneca, Novartis, and Johnson & Johnson.[6]

She was appointed as Head of Regulation of Medicines and other Health Technologies with the World Health Organization (WHO) in 2016,.[3] In November 2020 she was appointed Executive Director of the EMA,[1] also taking the position of chairperson at the International Coalition of Medicines Regulatory Authorities (ICMRA) at the same time.[2]

On 16 March 2021, Cooke led an EMA press conference to inform about the ongoing investigation into reports of side-effects related to the Oxford–AstraZeneca COVID-19 vaccine. Cooke said the EMA remains "firmly convinced" that the vaccine benefits outweigh the risks of potential side effects.