Lisa Smith, from Co Louth, has been charged with membership of an unlawful organisation under 2005 terror legislation.
The 38-year-old appeared at Dublin District Court on Friday.
The court heard Smith faces an additional charge of terrorist financing. This relates to an alleged offence within the Irish state in 2015 in the sum of 800 euros.
Smith was in court on Friday to be served the book of evidence but her defence solicitor Peter Corrigan said he was seeking a one-week adjournment.
Mr Corrigan said Smith has been denied her fundamental right to a jury trial.
The court heard Smith was to have the book of evidence served on her on Friday but surety was not present.
Mr Corrigan said his client has been signing on at her local Garda station for the past seven months.
“She has complied (with) very stringent conditions,” he said.
As part of strict bail conditions set by the courts, Smith must reside at an address in the north east of the country and sign on at a Garda station twice daily from 10am-1pm and 3pm-6pm.
She was also ordered to obey a curfew and has to remain indoors from 8pm to 7am.
She has been banned from accessing the internet or using social media.
Smith, who wore an Islamic dress and hijab with her face uncovered in court, sat silently throughout her brief appearance.
Judge Grainne Malone adjourned the case until July 31st and remanded Smith on bail for one more week.
Smith was arrested at Dublin Airport in 2019 on suspicion of terrorist offences after returning from Turkey in November with her young daughter.
She had travelled to Syria a number of years ago after she converted to Islam.