A child arriving to Ireland at 14/15/16 will not be expected to study Irish for Leaving Cert.
But, most schools are timetabled to teach students 7 subjects for Leaving Certificate, including Irish. The very small handful of exempt students will not be offered another option regardless of the reason for their exemption. They will likely have to sit in the back of the classroom when Irish is being taught, they can use this time to study other subjects or to pick up some Irish language skills. For 5th year and Leaving Cert, Irish is timetabled at the same time across all LC student timetables, so with 6 homerooms there may be 8 Irish classes timetabled to cater for students at different levels of ability, Higher-level, Ordinary-level and LCVP.
So, straightaway, your DC will likely be limited to 6 subjects in a typical state school. Bear in mind that the best 6 subjects count for points, this could be significant if they have an off-day in one subject. So, it's best to do another subject too. My teen DC have options like Agricultural Science and Japanese available for 5th Year and LC as extra subjects, taught on the school premises outside of school hours but paid for privately. Many students take Music and Music Theory classes at a local music school as an extra subject.
Very few schools offer Arabic except perhaps in Dublin and the one or two Islamic schools in the 26 counties. Classes are usually available in the local mosque (scarce enough still) but you would have to check would these be spoken language and grammar classes only or would they offer sufficient skills to be able to tackle drama/poetry questions which will likely arise on the Leaving Cert paper.
If you are willing to broaden your scope you could look at co-ed boarding schools such as Bandon Grammar and Midleton College, both possibly offer boarding out with a local family as an option. Both a reasonable distance from Cork airport which would have some connectivity with major UK airports.
One of my daughters is in Transition Year this year and will have 6 German students in her year, each is being hosted by a local family. So it is worth approaching a school which looks good on paper to see if they can put you in touch with a local family/agency to arrange this. Maybe you would even consider sending your DC for TY, some schools have exceptional programmes.
It is worth having a look at the Parent Power surveys by The Sunday Times to see what the top feeder schools are. However, take the whole thing with a very large pinch of salt. Results are skewed in favour of private schools (you probably wouldn't send your very average child or SEN child there) gaelcholáiste (you almost certainly wouldn't send a dyslexic or SEN child there, wonderful and all as they are) and geographic proximity of school to universities and technological institutes (yes, your child is more likely to go to a university if there is one in your city). But, if a state school is sending 85% or more of its students to uni/tech then it is doing something right and any student should be in with a good chance of achieving the uni/tech course of choice.