Anna graduated from Russian State Humanities University with a degree in culture studies. She later received another degree from Strelka Institute for Media, Architecture and Design. Since 2001, she has held managerial positions in project management and development. From 2012 to 2013, Trapkova worked in Russia's Ministry of Culture as the deputy head of the Department for State Support of Culture and Folk Arts and as the head of the Department of Programme Modernization. She was previously in charge of developing innovative cultural centres. Between 2013–2014, Ms. Trapkova worked as a project manager at Rambler Internet Holding. From 2014 to 2017, she served as the deputy head of the Pushkin Museum where she oversaw development of the Museum Complex. From 2017 to 2019, Ms. Trapkova served as the deputy director for renovation and development at the Garage Museum. She was tasked with renovating the Hexagon Pavilion and construction of the Salute Playground at Gorky Park. On 2 July 2019, she was appointed CEO of the Museum of Moscow.