Also we are hosted
Theme deployments can be done via a tool called Jive Cloud Admin. You can request access in the Jive support group.
There is the ability to deploy a theme update where the application nodes are restarted one at a time called 'rolling restart'.
During the deployment, which will take ~30 minutes, the site will be available but slower than usual. So you'd want to deploy to production off hours if possible.
Please be sure to always deploy to UAT first.