While the decision of the ALJ is final, that decision may be appealed to the Superior Court. Your appeal is not a new hearing, but a review of the hearing that was conducted to determine if the judge made an error in applying the law.
You may also request a rehearing through the Executive Hearing Office. A rehearing request will only be granted if the reasons provided meet the requirements listed in Article 5 of the Arizona Administrative Code. A timely motion for rehearing will stay most agency actions until a judge makes a ruling on the motion. Contact the Executive Hearing Office if you have questions about whether a particular action will be stayed pending a rehearing request.