Criminal Procedure Act 2011, ss 229-232, 244, 247, 248, 250
You can appeal a fine to the High Court by appealing against the decision to find you guilty (appealing your conviction), or appealing against the decision to fine you (appealing your sentence), or both. You can also appeal the amount of the fine.
Usually you have to file your appeal within 20 working days after the judge’s decision to fine you.