Is there a way for me to have another hearing since I did not receive notification?

This question is missing critical information. If you are over 21 and this is your court date and you are charged with a misdemeanor, the cop doesn't have to show, the first appearance is an arraignment and you simply enter a plea and get a new court date, if you missed this date then you likely have an outstanding arrest warrant. If you requested a DMV hearing within 10 days of your arrest and the officer didn't show at the hearing then you should have selected a new date (over your objection) and you would have had notice of the new date. If this was a DUI Infraction hearing and the officer failed to show, you should have won. If you didn't win, then you should have been present in court when the new date was selected in which case, you had notice. A DUI lawyer in your area may be able to help you get a new hearing.

Was this a court hearing that you missed or an administrative hearing with the Secretary of State?

I would write and ask for another date and mention that they did not dismiss the case the first time when the cop did not show up.

That is the "lost in the mail" defense. Go to the court clerk for a copy of the notice. Look at the "proof of service".? Were you at that address at that time?? Tell the clerk the cop didn't appear the first time though he was supposed to. Did he have an excuse? So, then, you are entitled to another court date.

If you did not receive notice then no action can be taken against you.

There should be, engage an attorney to assist you.

The charge should have been dismissed the first time. You should see a DUI specialist lawyer immediately (which you should have done the first time).