How to respond if comments/suggestions/compliments brought by staff involves a “peer” and not a direct report?

Generally, we recommend that you coach the employee to approach the peer to give the feedback (so long as it is not a complaint of any kind of discrimination or prohibited harassment – such issues must be reported to HR) through role playing and other support. If the employee is not comfortable going directly to the peer, you should recommend that they go through their management chain.   If you are observing the same issues, then you should approach your peer directly based on what you observe yourself.