The new Nauru Court of Appeal was set to hear their application this week but it has been put off until next year, although a date is yet to be set.
The Nauru 19, which includes a former president of the country, had been charged over an anti-government protest more than three years ago.
In September the group successfully sought a permanent stay on legal proceedings against them, arguing the trial process had dragged on too long and that the government had not met a court order to meet some of the costs.
Justice Geoff Muecke had referred to the government‘s conduct throughout the lengthy legal process as a “shameful affront to the rule of law”.
Last week three of the group, who had already pleaded guilty, failed on appeal to overturn their sentences and they are now serving jail terms.