To set up a new ONTAP cluster, three crucial components are required: the cluster management IP, which is necessary for managing the cluster; the node management IP, which is used for managing individual nodes within the cluster; and the intercluster IP, which is needed for communication between clusters. These IPs ensure proper management and connectivity within and between clusters. Although a password is important for security purposes and Advanced Drive Partitioning might be useful for storage optimization, they are not fundamental requirements for the initial cluster setup.