Access rights are stored directly on the items.
You cannot move access rights assigned for a role or user to another environment using content packages without including those items inside content package.
Access rights for items is just one field there:
If you check raw values of that field, it's just a string value, e.g.:
You need to move that value to another environment. If you're limited to content packages, you need to move the item containing that field. If you have other options, you may try to copy value of that field only.