Irish Catholic priests or nuns, basically, turn up in a lot of places. It's like Ireland exports them.
This was indeed once very common back in The '50s and earlier when Ireland essentially did export clergy. In part this was due to the tradition of Irish priests and nuns going overseas both as students and missionaries and in part simply due to the very high emigration rate in Ireland (12.7 people per 1000 in 1950). It also runs with the stereotype, within Britain and the US, that Irish Catholics are particularly devout.
Having said that, this is definitely not the case today; changing demographics and the growth of secularism mean that these days, Ireland does not even train enough priests for her own needs, and has to import from Poland and Africa. Thus, unless the priest or nun is very elderly or is in a period piece, he or she is not too likely to be Irish. An exception is the United States, where even if priests who actually came from Ireland are fairly rare, Irish-descended clergy dominate the church hierarchy; there's a very good chance that any given American Catholic archbishop or Cardinal (both in fiction and reality) is Irish—it's something of a bit of a joke within the American Church that all the American Cardinals seem to trace at least part of their ancestry from the Emerald Isle.note However, the same is not true of the parishioners; religious surveys done within the last ten years show that Irish Americans are one of the most secularized ethnic communities in America.note In addition, having been born and raised in America, Irish priests are unlikely to have a heavy Irish accent despite what you find on TV.
In terms of rank, the authority tropes arguably equal are Badass Preacher, Corrupt Corporate Executive, Landlord, Preacher Man, Pedophile Priest, Schoolteachers Sexy Priest, Sinister Minister and The Vicar. For the next step down, see Student Council President. For the next step up, see Dean Bitterman.
- Monsignor Ryan from Angel Of The Bat is a priest of Irish descent, though he and his family have been in America long enough that he doesn't have many stereotypes attached to him.
- Tapper Smurf, the Oirish bartender in Empath: The Luckiest Smurf, becomes one in the latter years of his life, calling himself Pastor Nevin (a variant of his birth name Naomhán), during the framing story of "A Wedding To Remember". He isn't Catholic, though he does have some of its trappings like wearing a long black robe.
- Father Brennan in The Omen (1976).
- Father Barry in On the Waterfront.
- In Trading Places, Coleman dresses as one.
- In The Delta Force, a heartwarming moment as Father O'Malley says that he should be grouped with the Jewish hostages, because he considers himself both a Jew and a Christian.
- Father Everett in the Daredevil movie.
- Father Geoghagan in The Wild Geese.
- Father Delaney from the original The Amityville Horror (1979).
- Father Alex in Mamma Mia!.
- Father Janovich in Gran Torino. Despite the name, he's given an Irish lilt.
- A very memorable one is played by Liam Neeson in Gangs of New York.
- Though he wasn't an actual clergyman (just a very devout mobster), as Bill is quick to point out.
- In Million Dollar Baby, the character played by Clint Eastwood keeps pestering an Irish priest with intentionally silly questions about Catholic doctrine, even causing him to drop an F-bomb.
- Father Fitzgibbon in Going My Way played by Barry Fitzgerald defines this trope. He came over from the old country as a young man and yearns to visit Ireland again.
- Father Peter Lonergan and Father Paul in The Quiet Man. Of course, an Irish priest in 1920's Ireland doesn't exactly stick out.
- Lots of them show up in Spotlight, it being set in Boston.
- Mike Bennett's grandfather (he become a priest after he was widowed) Seamus in the James Patterson novel Step on a Crack.
- Father Wolfe in A Tale Etched In Blood And Hard Black Pencil.
- Father Luis Quinn in Ian McDonald's Brasyl.
- Baby Kochamma falls in love with one in The God of Small Things.
- Father Ralph of The Thorn Birds
- Father Callahan of 'Salem's Lot and The Dark Tower.
- Father Duddleswell in the original stories which inspired Bless Me Father
- Military thriller Victoria has Father Murphy, who memorably ministers to protagonist John Rumford and some new converts in the field during the battle for Boston.
- Caitlin O'Shaughnessy, in Airwolf, one pretended to be an Irish nun.
- Harry O'Rourke, Vatican investigator in the JAG episodes "Miracles" and "Salvation".
- Nick impersonates one in an episode of Forever Knight. He gets to hear Schanke's confession.
- Father Liam Riley from the Paris episodes of Highlander: The Raven.
- Father Mulcahy of Mash is of Irish heritage.
- Patrick Fitzpatrick of Veronica Mars. Also most likely a Corrupt Priest and a member of Irish Mafia.
- Sons of Anarchy featured a prominent Belfast priest who was one of the top leaders of the Real IRA.
- Ballykissangel lampshades this since it's (initially) about an English priest assigned to a parish in Ireland.
- One appeared in the Pedophile Priest episode of Law & Order: SVU
- One episode of Sharpe has an Irish priest in Spain, who turns out to be something of a badass.
- Father Ted is about three Priests (a drunkard, an idiot, and the title character) on an Irish island. This trope is invoked not so much Once an Episode as Once A Minute.
- In one episode, a nun gushes to a black priest about what wonderful work he must be doing among those poor Africans, and ask how the missions there are doing. The priest replies in a thick Irish accent: "Sure, I wouldn't know, I'm from Donegal."
- Though he's not a priest, Nate Ford from Leverage is Boston Irish and attended a seminary in his teenage years intending to become a priest. Him portraying clergy is a common occurance to the team's cons. We also meet one of his friends who is an Irish Priest.
- On iCarly, Sam Puckett is obsessed with meeting Father McGurthy, the world's fattest priest, combining both this trope and the show's perchance for Punny Names.
- Father Duddleswell in the TV sitcom Bless Me Father, based on original short stories (see Literature).
- In Frasier, the Seattle radio station's religious presenter is Father Mike, who in accent and demanour is affably Irish-American. Except for his surname being a Spanish one (Mendosa). This infers that all priests become Irish, regardless of ethnic origin.
- One appears on Good Eats, along with a rabbi. Alton asks the priest about corned beef in Ireland, and the priest replies that he doesn't eat it. The rabbi doesn't provide much insight into the origin of the dish, either. The nutritional anthropologist explains that a traditional dish in Ireland is bacon and cabbage. When Irish immigrants came to the US, bacon was out of the financial reach of many of them. But they did have lots of new Jewish neighbors, who couldn't eat bacon because of Kosher laws forbidding pork and pork products. They had lots of brisket, though, and showed their new Irish neighbors a way of preserving it that renders a meat product kind of, sort of like bacon. As a result, it became the replacement for bacon in the traditional dish in the US. (In fact, it's so popular that if St. Patrick's Day happens to fall on a Friday during Lent, when meat is forbidden to Catholics, the Catholic Church actually grants an exception to that rule for corned beef and cabbage!)
- Tommy Tiernan has a bit on this.
We used to grow priests in Ireland. We used to grow them from bits of people that we didn't like. But we over-planted. We had an epidemic. We were flooded with them. So, we tried to engage the rest of the world in a priest-for-potato swap. And we were conned by the Africans. Bastards! Took all our priests, not a potato between them. Pagan spudless fuckers! Our priests went over to Africa, and what happened? What do you think happened? They melted! And now we've run out of priests in Ireland. There's none left. And irony of ironies, what's happening? Missionaries! From Africa!
- A Rubber Chicken Films sketch  features a classic Irish priest.
- OneGirl Genius plot-arc features Brother Ulm, a monk in the Corbettites, a monastic order devoted to operating a politically neutral free-to-all rail liner service throughout Europa. He serves as the conductor aboard the Wyrm of Limerick, and eventually has his consciousness transferred and becomes the controlling intellect on a new super-train.
- It seems that at least half of Springfield's Catholic clergy in The Simpsons is Irish.
- And one of them is actually voiced by Liam Neeson.
- Played with in the Batman: The Animated Series episode "Trial", where the Joker dresses up as a priest and assumes a thick Irish accent to take Batman's "confession" before the villains (attempt to) kill him.