By approximately 6 years of age, children can use time-based visual selection to ignore stationary stimuli, already in the visual field and prioritize the selection of newly arriving stimuli. This ability can be studied using preview search, a version of the visual search paradigm with an added temporal component, in which one set of distractors is presented (previewed) before a second set that contains the target item. Preview search is more efficient than if all items are presented simultaneously, suggesting that temporally "old" objects can be ignored (the preview benefit). In two experiments, we examined the developmental trajectory for time-based visual selection in a sample of 192 6-, 8-, and 12-year-old children (49% female, predominantly White), with adults as controls (75% female, predominantly White), in the United Kingdom. The results showed an absence of the ability to ignore previewed moving distractors in 6-year-olds and confirmed its presence from 8 years of age. However, full development of this ability, which includes maintaining inhibition of previewed items over extended periods, was only present from the age of 12. Individual differences in executive functions, namely inhibition, were associated with preview search efficiency in 6-year-olds and adults. Overall, the results suggest a developmental trajectory in the ability to ignore moving old objects that occurs in two stages and develops later than the ability to ignore previewed stationary objects. The results are discussed in terms of underlying inhibitory mechanisms, in addition to individual differences in the expression of this ability.