Is there a server event for when an actor gets replicated to the owning client?

Is there a way to get notified on the server when the client receives the actor from the server? I know I can just do a server RPC in the client’s constructor to notify the server, but I was wondering if there is some event that already gets triggered that I can use.

There isn’t - stricly speaking the Server shouldn’t care if a client does/doesn’t have an actor at a given time.

Either way calling an RPC from constructor isn’t safe, you’d need to use BeginPlay() or something similar.