She was arrested at 10.30 this morning and charged with committing a terrorist offence outside the Irish state between 28 October, 2015 and 1 December, 2019.
Ms Smith denies the allegations.
This is the first case of this nature in the Republic of Ireland. Ms Smith, 38, has a two-year-old daughter who is now being cared for by relatives.
The former member of the Irish defence force, who was wearing a black burqa during the hearing, made no comment when she was charged.
Her application for bail was heard in-camera at the request of prosecution counsel.
The Director of Public Prospection said the state could not disclose its case publicly because it contained sensitive details that could be prejudicial to a future trial.
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