Your mother is an Irish citizen with or without a passport. It doesn’t matter either way. You would have to live in Ireland for three years at least to be able to apply for naturalisation with your mother’s Irish association, or five years if you are to apply on your own.
The official website summed it up well pretty much:
https://www.irishimmigration.ie/citizen ... ociations/
Applications for naturalisation are often received where the applicant seeks the Minister to exercise absolute discretion under Section 16 of the Irish Nationality and Citizenship Act 1956, as amended to waive the statutory conditions on the basis of Irish descent or Irish associations going back two, three or indeed more generations. An association going back two generations without any other link to the State is generally considered as not sufficient to warrant consideration or the waiving of the statutory residence conditions.
Applicants who seek to avail of the discretion provided under Section 16 of the Act are expected to have a reasonable period of lawful residence in the State, generally around 3 years, to show they have some substantial and tangible connection with Irish society and the State.
An Irish association through a great-grandparent, (or a grandparent where that grandparent obtained citizenship through naturalisation) and where there is no, or negligible, reckonable residency would generally be deemed insufficient to warrant recommending the Minister exercise absolute discretion to waive the statutory conditions under Section 15 of the Irish Nationality and Citizenship Act 1956, as amended and would result in a refusal.
In general, had your mother not been an Irish citizen, you would have to get 5 years of residence. With your mother being Irish, you have a chance of having 2 of 5 years waived by the minister. However, this is not guaranteed and that you must show evidence that you are actively engaging in the Irish community (working/studying etc) for these 3 years.
