Reboot standby

We have 2 postgres servers, a primary and standby. One of our DB admins noticed a "health indicator" alert light on our standby which means "system degraded." She logged into the iLO and it lists the Cache Module Status as Failed. This needs to be repaired (we have an idea on what needs to be done) and most likely will require a reboot of our standby server.

We use streaming replication and from what I can see, that is initiated by the standby server. What are the shutdown and restart considerations for our standby server?