AI-enabled synthetic biology has tremendous potential but also significantly increases biorisks and brings about a new set of dual use concerns. The picture is complicated given the vast innovations envisioned to emerge by combining emerging technologies, as AI-enabled synthetic biology potentially scales up bioengineering into industrial biomanufacturing. However, the literature review indicates that goals such as maintaining a reasonable scope for innovation, or more ambitiously to foster a huge bioeconomy do not necessarily contrast with biosafety, but need to go hand in hand. This paper presents a literature review of the issues and describes emerging frameworks for policy and practice that transverse the options of command-and-control, stewardship, bottom-up, and laissez-faire governance. How to achieve early warning systems that enable prevention and mitigation of future AI-enabled biohazards from the lab, from deliberate misuse, or from the public realm, will constantly need to evolve, and adaptive, interactive approaches should emerge. Although biorisk is subject to an established governance regime, and scientists generally adhere to biosafety protocols, even experimental, but legitimate use by scientists could lead to unexpected developments. Recent advances in chatbots enabled by generative AI have revived fears that advanced biological insight can more easily get into the hands of malignant individuals or organizations. Given these sets of issues, society needs to rethink how AI-enabled synthetic biology should be governed. The suggested way to visualize the challenge at hand is whack-a-mole governance, although the emerging solutions are perhaps not so different either.