Although natural selection often fluctuates across ontogeny, it remains unclear what conditions enable selection in one life-cycle stage to shape evolution in others. Organisms that undergo metamorphosis are useful for addressing this topic because their highly specialized life-cycle stages cannot always evolve independently despite their dramatic life-history transition. Using a comparative study of dragonflies, we examined three conditions that are hypothesized to allow selection in one stage to affect evolution in others. First, we tested whether lineages with less dramatic metamorphosis (e.g., hemimetabolous insects) lack the capacity for stage-specific evolution. Rejecting this hypothesis, we found that larval body shape evolves independently from selection on adult shape. Next, we evaluated whether stage-specific evolution is limited for homologous and/or coadapted structures. Indeed, we found that selection for larger wings is associated with the evolution of coadapted larval sheaths that store developing wing tissue. Finally, we assessed whether stage-specific evolution is restricted for traits linked to a single biochemical pathway. Supporting this hypothesis, we found that species with more wing melanization in the adult stage have evolved weaker melanin immune defenses in the larval stage. Thus, our results collectively show that natural selection in one stage imposes trait-dependent constraints on evolution in others.