You can sync roles between CiviCRM and Drupal to share useful information. Using the setup detailed below, you could for instance create a group of all your members in CiviCRM that you synced to a Member role in Drupal. You would then easily be able to set permissions in Drupal for all members based on the information updated automatically from CiviCRM.
The civicrm_group_roles and civicrm_member_roles modules are included with the CiviCRM module.


IMPORTANT NOTE: The New, Current, and Grace setting do not override Expired and Pending. There is another status of Canceled that can be used to when a user with one type membership let it expire and rather than renew, creates a new membership that's a different kind. If there is one expired membership, it will remove the user from the role.
While you can manually and automatically sync CiviMember_roles there is no option to do so for CiviGroup_roles which will only sync when a user logs into their Drupal account.