Create a valid dump of your local postgres database and host it somewhere publicly available. Now you will be able to restore this entire dataset (schema and records) with pg:backups:restore as shown here. The sole caveat here is that the target database must be completely empty for this to work. You can empty a Heroku postgres database with heroku pg:reset.
If you cannot take the approach listed above then you can run pg_restore directly from your local instance, provided your local version of Postgres is >= the target version of Postgres. This also applies to creating the dumpfile and is a requirement because pg utilities are not guaranteed to be forward compatible. Documentation for pg_restore is here.