Lisa Smith (39) had been due to go on trial at the Special Criminal Court on Tuesday but the court will instead hear an application from her lawyers for the case to be dismissed.
They are expected to argue there is not sufficient evidence to put her on trial.
Her case received widespread attention when it emerged in March 2019 that Smith, a former member of the Air Corps who served on the government jet, was detained in Syria over alleged links to Islamic State.
She was returned to Ireland that December and subsequently charged with membership of an unlawful terrorist group, Islamic State (ISIS), between October 28, 2015 and December 1, 2019.
Smith was also charged with financing terrorism by sending €800 in assistance, via a Western Union money transfer, to a named man on May 6, 2015.
She has denied the charges.
Smith’s application to dismiss the charges is being made under a section of the Criminal Procedure Act 1967.
This allows a trial court to dismiss charges where it considers there is not a sufficient case to put the accused on trial.
The grounds for the application are set to be revealed in court on Tuesday.
Smith joined the Defence Forces after leaving school in 2000 and also served with the Air Corps.
After converting to Islam she left Ireland in 2015.
A caliphate – a state governed in accordance with Islamic law, or Sharia – had been declared and Islamic State seized large swathes of territory in Syria and Iraq.
Smith’s barrister, Michael O’Higgins SC, has previously told the Special Criminal Court that she travelled around the Middle East and found herself in the area where the caliphate was declared.
The barrister said anyone voluntarily living there made them "automatically" a member of ISIS.
Should the application fail, the trial is likely to get underway later this week and is expected to last for 12 weeks.
The trial would involve evidence from a number of international witnesses.
Last November the court said it would allow evidence to be called from three witnesses by video-link as it was either "undesirable or not possible" for them to travel to Ireland. Two of the witnesses are in Australia while another is in the US.