Criminal Procedure Act 2011, s 177
If the judge fined you after convicting you at a hearing you attended, they have the discretion to order a rehearing, either of the whole case or just of the fine.
When they’re deciding whether to order a rehearing, the main question for the judge is whether there’s been a “miscarriage of justice” – in other words, whether there was something unfair about the process.
This could be, for example, if some of the evidence the judge relied on wasn’t legally allowed to be presented in court (“not admissible”), or if the judge made a mistake in interpreting the relevant law, or if the judge or the prosecution lawyer behaved improperly at the trial.
Criminal Procedure Act 2011, ss 125, 126
If the judge fined you after convicting you in your absence, and you didn’t know the court hearing was happening, you have the right to a rehearing. If you did know about the hearing but couldn’t be there for a good reason or if you have a defence, you can apply for a rehearing.