This answer assumes that you're using Heroku CLI. Any instance of "YOUR_APP_NAME" in a command should be replaced by the application name of the Heroku App you're working with.
You will also need on hand the connection URL (shown here as DATABASE_URL) of your current hobby-dev database to be upgraded.
1. Provision a new hobby-basic database:
heroku addons:create heroku-postgresql:hobby-basic -a YOUR_APP_NAME
This will output a name for the new database containing a color. You will need to refer to this later. For example:
HEROKU_POSTGRESQL_PINK_URL
2. Optionally put db into maintenance mode to ensure that no data is added to the db while it's being copied.
heroku maintenance:on --app YOUR_APP_NAME
3. Copy the existing hobby-dev db to the hobby-basic db
heroku pg:copy DATABASE_URL HEROKU_POSTGRESQL_PINK --app YOUR_APP_NAME
Heroku will now print the following message.
heroku pg:copy DATABASE_URL HEROKU_POSTGRESQL_PINK --app YOUR_APP_NAME
! WARNING: Destructive Action
! Transfering data from DATABASE_URL to HEROKU_POSTGRESQL_PINK
! This command will affect the app: YOUR_APP_NAME
! To proceed, type "YOUR_APP_NAME" or re-run this command with --confirm YOUR_APP_NAME
YOUR_APP_NAME
4. Confirm db transfer by typing the actual name of your application
YOUR_APP_NAME
5. Promote your new database
heroku pg:promote HEROKU_POSTGRESQL_PINK --app YOUR_APP_NAME
The color-based name of the database you promote should be copied from the output you got up in step 1. Do not copy and paste the line above word for word, it will not work.
6. If you put your db into maintenance mode earlier, turn it off.
heroku maintenance:off --app YOUR_APP_NAME