Trade-offs play an important role in evolution. Without trade-offs, evolution would maximize fitness of all traits leading to a "master of all traits". The shape of trade-offs has been shown to determine evolutionary trajectories and is often assumed to be static and independent of the actual evolutionary process. Here we propose that coevolution leads to a dynamical trade-off. We test this hypothesis in a microbial predator-prey system and show that the bacterial growth-defense trade-off changes from concave to convex, i.e., defense is effective and cheap initially, but gets costly when predators coevolve. We further explore the impact of such dynamical trade-offs by a novel mathematical model incorporating de novo mutations for both species. Predator and prey populations diversify rapidly leading to higher prey diversity when the trade-off is concave (cheap). Coevolution results in more convex (costly) trade-offs and lower prey diversity compared to the scenario where only the prey evolves.