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1. Dispersal is a key process in population biology and ecology. Although the general ecological conditions that lead to dispersal have been well studied, the causes of individual variation in dispersal are less well understood. A number of recent studies suggest that heritable temperament – or personality – traits are correlated with dispersal in the wild but the extent to which these ‘personality-dispersal syndromes’ are general, how they depend on an individual's state and on spatial scale and whether they are temporally stable, both within and across individuals, remains unclear.2. Here, we examine the relationship between exploration behaviour – an axis of personality that appears to be important in animals generally – and a variety of dispersal processes over 6 years in a population of the great tit Parus major.3. Exploration behaviour was higher in immigrant than in locally born juveniles, but the difference was much larger for individuals with a small body mass, though independent of sex, representing one of the first examples of a state-dependent effect in a personality-dispersal syndrome.4. Despite a temporal trend in exploration behaviour at the population level, the difference between immigrants and locally born birds remained stable over time, both across and within individuals. This suggests that the personality difference between immigrants and locally born birds is established early in development, but that the process of immigration interacts with both personality and state.5. We found that the number of immigrant parents a locally born bird had did not influence exploration behaviour, suggesting either the difference between immigrants and residents was environmental or that the effect is overridden by local environmental sources of variation.6. In contrast to previous work, we found no evidence for links between personality and natal dispersal distance within the population, either in terms of an individual's own exploration behaviour or that of its parents.7. Our results suggest that there are links between individual differences in personality and dispersal, but that these can be dependent on differences in state among individuals and on the scale over which dispersal is measured. Future work should aim to understand the differences between dispersal within and between populations and the ways in which personality and state interact to determine the outcome of these processes.