Astilbes should be pruned in the early spring after the last frost. Pruning them in early summer is an option but the longer you wait the more flowers could be lost to the prune. You can prune off spent flowers to keep your plant looking tidy but too much pruning late in the season can spur new growth that is delicate and may be killed off by frosts in the fall and winter and cause undo stress to the plant as well as an unsightly plant.