There a few options for users with Gmail Storage reaching capacity; 

  1. Delete old messages with attachment - (screenshot)
  2. Create a new "", then migrate the oldest mail to  After the migration, delegate access of "" to "".  That makes it fairly straight forward for them to access their historical mail.  You can also set the default send as in the "" account to be "" .  That way if they do need to reply to any historical mail they could do so.           *for additional information on the migration process email