Antimicrobial resistance (AMR) should be tackled through a One Health approach, as stated in the World Health Organization Global Action Plan on AMR. We describe the landscape of AMR surveillance in the European Union/European Economic Area (EU/EEA) and underline a gap regarding veterinary medicine. Current AMR surveillance efforts are of limited help to veterinary practitioners and policymakers seeking to improve antimicrobial stewardship in animal health. We propose to establish the European Antimicrobial Resistance Surveillance network in Veterinary medicine (EARS-Vet) to report on the AMR situation, follow AMR trends and detect emerging AMR in selected bacterial pathogens of animals. This information could be useful to advise policymakers, explore efficacy of interventions, support antimicrobial stewardship initiatives, (re-)evaluate marketing authorisations of antimicrobials, generate epidemiological cut-off values, assess risk of zoonotic AMR transmission and evaluate the burden of AMR in animal health. EARS-Vet could be integrated with other AMR monitoring systems in the animal and medical sectors to ensure a One Health approach. Herein, we present a strategy to establish EARS-Vet as a network of national surveillance systems and highlight challenges of data harmonisation and bias. Strong political commitment at national and EU/EEA levels is required for the success of EARS-Vet.