The FIDE ratings page here, which shows the highest FIDE ratings achieved by Irish players, ranked in descending order, has been updated to account for the May and June 2023 lists.
Conor Murphy moved from 2450 to 2454 in May (unchanged in 4th place), while Trisha Kanyamarala moved sharply upwards in June from her previous best of 2299 (38th place) to 2344 (23rd place).
Trisha clearly qualifies for the FM title now, but I am fairly sure that she had previously crossed 2300 in live rating around the time that she had a published rating of 2299.
I also added two Irish players I had previously missed.
Eugene J. Gibney is best known as a correspondence player. He was Irish correspondence champion four times, in 1980, 1981, 1985, and 1991 (see list), and became a Correspondence Chess Senior International Master in 2004. He has represented Ireland many times in Correspondence Chess Olympiads and other team tournaments. However, he also played over the board, and was FIDE rated as 2281 in October 2000, registered as Canadian (he has lived in Lloydminster, Canada for many years), placing him 50th in this list. (The ICCA web pages have an interview with him.)
In addition, I was previously uncertain whether Gerard McDonnell of Castlebar was the same person as the player, with USA nationality, rated 2285 in the January 2000 list. The latter player was born in 1960, and as I recalled playing in a Glorney Cup team with Gerard of Castlebar in 1979, it seemed as if the age didn’t quite match. Also, Gerard of Castlebar’s rating in his Irish playing days was lower—for example, his ICU rating in the 1983 list was 2031—and that seemed a large jump. However, I noticed recently that the Castlebar and USA players have the same birthday. I also recall that the cutoff for Glorney Cup eligibility was being under 19 in August of the relevant year. I assume this must be the same player, and he enters the list at joint 45th-48th places.