Trait curiosity is an intrinsic drive for acquiring knowledge and experience, which motivates learning and exploration. The trait’s expression varies between individuals and is known to decline with age. In the present study, we examined how individual differences in trait curiosity and age influence speed and incidental learning in a hybrid visual and memory search task. Hybrid search is akin to many real-world searches and requires the observer to look for multiple, previously memorized, target objects among distractors objects. In three experiments, participants memorized and searched for four targets. Targets were presented in a fixed sequence over search trials in one block (incidental learning condition), and in random order in the other (no-learning condition). We found that effects of trait curiosity on search performance varied with age: Curiosity was linked to incidental learning effects, however, only in young participants who remained unaware of the sequence. By contrast, trait curiosity did not impact search speed in young adults. Conversely, in middle-to-older aged adults, curiosity was unrelated to learning effects, but associated with faster search speed. Furthermore, the effect of curiosity on speed was partially mediated by age. This suggests that age-related decline in curiosity contributes to slower search speed, but also that curiosity may act as a partial buffer against age-related slowing. Together, our results support the notion that trait curiosity can benefit cognition, and that the curiosity-cognition relationship varies with age.