for(Case caseLoop : Trigger.new){
   Case oldCase = Trigger.OldMap.get(caseLoop.id);
}

Public class className extends TriggerHandler{
   public override void afterUpdate() {
      afterUpdateLogics();
   }

   public static void afterUpdateLogics(){
      for(Case caseLoop : (List<Case>) Trigger.new){
          ***Needs to get the old map here****
      }
   }
}