Assessing the evolutionary potential of animal populations in the wild is crucial to understanding how they may respond to selection mediated by rapid environmental change (e.g. habitat loss and fragmentation). A growing number of studies have investigated the adaptive role of behaviour, but assessments of its genetic basis in a natural setting remain scarce. We combined intensive biologging technology with genome-wide data and a pedigree-free quantitative genetic approach to quantify repeatability, heritability and evolvability for a suite of behaviours related to the risk avoidance-resource acquisition trade-off in a wild roe deer (Capreolus capreolus) population inhabiting a heterogeneous, human-dominated landscape. These traits, linked to the stress response, movement and space-use behaviour, were all moderately to highly repeatable. Furthermore, the repeatable among-individual component of variation in these traits was partly due to additive genetic variance, with heritability estimates ranging from 0.19±0.07 to 0.71±0.11 and evolvability ranging from 1.1 to 4.3%. Changes in the trait mean can therefore occur under hypothetical directional selection over just a few generations. To the best of our knowledge, this is the first empirical demonstration of additive genetic variation in space-use behaviour in a free-ranging population based on genomic relatedness data. We conclude that wild animal populations may have the potential to adjust their spatial behaviour to human-driven environmental modifications through micro-evolutionary change.