On the Pine site they've posted a quick tutorial showing how to host private packages on Gitlab, in their case it's for Laravel-related packages but it would work with any project making use of Composer for package management.

When we want to restrict the access to the package we made but we don’t want to pay for a service like Private Packagist, we can use tagged: hosting gitlab private package accesstoken tutorial composer configuration

Link: https://pineco.de/hosting-private-laravel-packages-gitlab/