Individual consistency in behaviour, known as animal personality, and behavioural plasticity in response to environmental changes are important factors shaping individual behaviour. Correlations between them, called personality-dependent plasticity, indicate that personality can affect individual reactions to the environment. In farm animals this could impact the response to management changes or stressors but has not yet been investigated. Here we use ultra-wideband location sensors to measure personality and plasticity in the movement of 90 dairy calves for up to 56 days starting in small pair-housing enclosures, and subsequently moved to larger social housings. For the first time calves were shown to differ in personality and plasticity of movement when changing housing. There were significant correlations between personality and plasticity for distance travelled (0.57), meaning that individuals that travelled the furthest in the pair housing increased their movement more in the social groups, and for residence time (− 0.65) as those that stayed in the same area more decreased more with the change in housing, demonstrating personality-dependent plasticity. Additionally, calves conformed to their pen-mate’s behaviour in pairs, but this did not continue in the groups. Therefore, personality, plasticity and social effects impact how farm animals respond to changes and can inform management decisions.