New Ireland apparently has two meanings in New Brunswick. When the separation from Nova Scotia was proposed in 1784, William Knox, himself Irish, suggested New Ireland as the name of the new province. The Irish, however, being such a troublesome and rebellious people, and considering recent events in that part of North America, it was felt that name would be inauspicious.
There was, possibly as early as 1827 and as late as 1905, a New Ireland in Albert Co.
Tom Collins wrote at:
http://www.virtualmuseum.ca/pm.php?id=story_line&lg=Engl...

The area of Albert County known as New Ireland is today nothing more than miles and miles of woodlands dotted by the occasional hunting cabin. Very few signs of settlement of the area by the Irish in the early 1800's still exist, except for the Catholic cemetery located next to the spot where the Catholic church once stood, and the names of the roads, hills, and other locations in the area, like Teahans Corner, which offer a hint of the Irish immigrants who settled this land and called it New Ireland. Father McAuley, the Catholic priest for the area, and much of the county, had supervised the construction of the Catholic church and rectory.

'Tom Collins' may be named in jest, as a history/mystery, "The Rectory Murder", referes to:

In New Brunswick's Hopewell Cape courthouse a sensational turn-of-the-century trial put young, handsome Tom Collins in the prisoner's dock. Collins was charged with the grisly murder of Mary Ann McAuley, housekeeper to the New Ireland parish priest. Newspaper reporters carefully chronicled every detail revealed in court of how the victim met her death.

and places the area near Riverview, NB. Another reference to its location is:

My wife's mother was born and brought up on Teahan's Corner in New Ireland. Teahan's Corner is located at the intersection of the Shepody road and the Forty Five road. We are currently clearing land on the corner and elsewhere in New Ireland.

The place apparently still exists as, at:

http://www.virtualmuseum.ca/pm.php?id=story_line&lg=Engl...

is a photo of the Shepody Marsh from Canada Hill in New Ireland.

Albert Co. was not the only area to have a New Ireland, as in 1840, 10 pounds was allocated for the road from Schovil Robert's Corner to New Ireland in Hampstead Parish, Queens Co. Also 10 pounds for the road from New Ireland to Sanburn's Mill.
New Ireland in Albert Co. is in Alma Parish, and about 1830 many Irish emigrants settled along the Shepody Bay Road. Apparently some religious conflict developed, and in 1832, the Protestant Irish moved to Sinclair Hill and Hebron. Alma Parish was created in 1835 from part of Harvey Parish. The petition of Bernard Duffy, of New Ireland, Harvey Parish, in 1847, is at:
http://homepages.rootsweb.com/~nbpast/AL/al-02.html
and states there were about 400 persons there at the time. Other members of the community subscribed their names in support of the petition for a grist mill. The population must have diminished over the next decades as in 1866 there were 68 families, and in 1871 there were about 150 persons. In 1898, the population was about 100. It was apparently abandoned in 1920, and much of it is contained in Fundy National Park.
There is a relatively recent book, "New Ireland Remembered: historical essays on the Irish in New Brunswick", ed. P. M. Toner, New Ireland Press (approriately enough), 217 Aberdeen Street, Fredericton, NB, Canada E3B 1R6. (I think New Ireland Press was named for the province, rather than the settlement.)
Robert F. Fellows extensive notes on Irish families in New Brunswick can be found at a wonderful site at;
http://www.newirelandnb.ca/nb_irish_family_names.html
This includes lists of many of these families found by clicking at the top on 'The Irish in NB - Local Histories', and then on 'Founding Irish Family Histories'.

Thomas