The defendant can appeal against a finding of guilt and/or the sentence imposed. The DPP normally can only appeal against the sentence imposed. There is no right of appeal against an acquittal in the Supreme Court. The DPP can apply to have an acquittal by a Magistrate reviewed in some cases. Any appeal must be lodged within 28 days of the Court's decision.
The DPP should talk to you about their decision to appeal.
You have a right to information about an appeal and the outcome.