AWS RDS MySQL migration from default VPC to custom VPC

I have an AWS RDS MySQL in one of the Public Subnets of one of the default VPCs. What would be the best and smooth procedure to migrate it to an RDS MySQL located in a new custom VPC in a private subnet? Would it be possible to create a VPC peering between both VPCs and then create an RDS Standby?

Thanks!

Solution

Create a Snapshot
Restore the database, select the custom VPC in the settings.
Update the new endpoint in your applications.

(or)

You can modify the DB settings and apply it in the next maintenance window

https://aws.amazon.com/premiumsupport/knowledge-center/change-vpc-rds-db-instance/