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The rapid progress that plasma wakefield accelerators are experiencing is now posing the question as to whether they could be included in the design of the next generation of high-energy electron-positron colliders. However, the typical structure of the accelerating wakefields presents challenging complications for positron acceleration. Despite seminal proof-of-principle experiments and theoretical proposals, experimental research in plasma-based acceleration of positrons is currently limited by the scarcity of positron beams suitable to seed a plasma accelerator. Here, we report on the first experimental demonstration of a laser-driven source of ultra-relativistic positrons with sufficient spectral and spatial quality to be injected in a plasma accelerator. Our results indicate, in agreement with numerical simulations, selection and transport of positron beamlets containing$$N_{e+}\ge 10^5$$$N_{e+}\ge {10}^5$positrons in a 5% bandwidth around 600 MeV, with femtosecond-scale duration and micron-scale normalised emittance. Particle-in-cell simulations show that positron beams of this kind can be guided and accelerated in a laser-driven plasma accelerator, with favourable scalings to further increase overall charge and energy using PW-scale lasers. The results presented here demonstrate the possibility of performing experimental studies of positron acceleration in a laser-driven wakefield accelerator.