To display a list of existing routers, use the openstack router list command shown here:
openstack router list
[--name <name>] [--enable | --disable] [--long]
[--project <project>]
[--project-domain <project-domain>]
[--agent <agent-id>] [--tags <tag>[,<tag>,...]]
[--any-tags <tag>[,<tag>,...]]
[--not-tags <tag>[,<tag>,...]]
[--not-any-tags <tag>[,<tag>,...]]
Filters based on name, project, admin state, scheduled agent, and tags can be used to narrow returned results.
Users will only see routers associated with their project. When executed as a user with the admin role, Neutron will return a listing of all routers across all projects unless a project ID is specified.