She can apply for an Irish passport if she is an Irish citizen. If she or her one of her parents was born on the island of Ireland, including Northern Ireland, she is a most likely an Irish citizen. In those cases, she can apply for a passport.
If one of her grandparents was born in Ireland, she can apply for citizenship by Foreign Birth Registration. When that is completed, she can apply for a passport.
Otherwise, she has to apply for citizenship via naturalisation. If you are an Irish citizen, she must have had three years residency in Ireland (naturalisation normally requires five years residency).
There's lots of information online. Try
here and
here.