migrating from a local PostgreSQL database to Amazon Aurora
As per @Pavel Tsiukhtsiayeu blog documentation Migrating PostgreSQL standalone instance to Aurora (Amazon RDS) The idea behind migration is simple: create Aurora cluster in RDS, setup database source and target endpoints at DMS, and launch database migration task. The data migration task will migrate all data from the source database, and replicate ongoing changes to the target endpoint. All you have to do is to point your web server to the new Aurora cluster, and hot reload web server once the source and target endpoints completely in sync.

For further your reference here