Is there any way to move existing database instance to a new cluster?

We have a scenario where we have multiple database instances and we need to add read replica and failover. We understand that it will be easy if we can have a New Cluster created and databases (writer and reader) within the newly created cluster and configure the failover priorities. Then take the snapshot of the old database and restore it to the newly created database with the cluster

Is there any way to avoid the above steps? Can we link the existing database instance to the new cluster?