Computer-use agents extend language models from text generation to sustained interaction with files, terminals, browsers, and external tools. This shift creates safety risks that are difficult to detect from isolated prompts or final responses, because harm often emerges only through multi-step execution traces whose individual actions appear locally benign. We introduce BraveGuard, a self-evolving defense framework for training guard models from open-world threat signals and realistic agent trajectories. BraveGuard mines recent research sources to identify emerging risks and attack patterns, instantiates them as executable computer-use tasks, collects agent rollouts, and derives trajectory-level supervision for guard model training. As new threats and validation failures appear, the pipeline can be repeated, yielding an adaptive defense loop rather than a static, benchmark-driven training process. We instantiate BraveGuard by training multiple guard backbones, including Qwen3-Guard and Llama-Guard variants, and evaluate the resulting guards on trajectory-level agent-safety benchmarks. BraveGuard consistently improves safety detection across computer-use trajectories. On AgentHazard, it substantially improves detection accuracy over off-the-shelf guard models, with accuracy increasing from 38.79% to 82.38% under the averaged guard-model setting. These results show that guard supervision grounded in open-world threat discovery and realistic agent execution can improve safety monitoring beyond fixed taxonomies and synthetic prompt-level data. BraveGuard offers a scalable path toward adaptive defenses for computer-use agents facing evolving real-world risks.