Change your database RDS instance security group to allow your machine to access it.
Add your ip to the security group to acces the instance via Postgres.
Make a copy of the database using pg_dump
$ pg_dump -h <public dns> -U <my username> -f <name of dump file .sql> <name of my database>
you will be asked for postgressql password.
a dump file(.sql) will be created
Restore that dump file to your local database.
but you might need to drop the database and create it first
$ psql -U <postgresql username> -d <database name> -f <dump file that you want to restore>
the database is restored
pg_restore -h <host> -U <username> -c -d <database name> <filename to be restored>

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