Your Q suggests you don't know but as a US citizen you remain subject to US tax -- even if resident elsewhere, and even if you have other (dual) citizenship. US is notoriously the only major country whose tax system works this way. The only way you get out of the US tax system is to renounce or lose your citizenship -- and if you do that with moderately high income and assets, you pay a special 'expatriation' tax, effectively in lieu of the taxes you would have paid for several future years if you had remained in the system.
You can get some benefits -- if you have earned income (from a job other than as a US government employee, or a trade) from a foreign country and live there, you can use the Foreign Earned Income Exclusion to exclude from US tax up to a limit ($103,900 for 2018, later years will adjust for inflation). But you still must file a return and report that income, adding form 2555 (or 2555-EZ) to claim the exclusion. And for income subject to both US and foreign tax -- nonearned income like investments, or earned income over the limit -- you can take either a deduction or credit on your US tax for the foreign tax; the credit is limited to the amount of US tax (figured per income category), but is more valuable to most people because it reduces tax by 100% instead of your marginal rate, now typically 22%-32%. And you get an automatic 2-month extension of the filing deadline without requesting on 4868, big whoop.
And you must report foreign bank accounts and financial assets if they exceed thresholds, under two different schemes. Under the older scheme created by the Bank Secrecy Act of 1970, if you own or control non-US bank accounts totalling over USD 10k during a year -- which if you are living there you almost certainly need to -- you must file 'FBAR' (Foreign Bank Account Report) to FinCEN (not IRS) (until a few years ago this was Form 114 on paper). Since people continued to cheat on their taxes even after BSA, in 2010 Congress passed the Foreign Account Tax Compliance Act, FATCA. The main new thing in FATCA is that non-US banks must report to IRS accounts owned by (apparent) US persons. Wait, you say, US doesn't have jurisdiction over non-US banks? Ha ha, that's a good one, it makes no difference to Congress. As a result you may well find that Irish banks who recognize you as a US citizen aren't eager for your business because of the extra work and risk to them from FATCA -- although since you presumably use Irish id and address they may not recognize you. But FATCA also requires additional reporting by anyone who is a US citizen, 'green-card' holder (LPR) or tax resident, on form 8938 added to your income tax return, of a rather broader set of foreign assets if they exceed a significantly higher threshold that depends on whether you live abroad (you do) and whether you are married and file jointly (you didn't say, and that in turn depends partly on whether your spouse is a US citizen). I recommend this nice summary page on the IRS website. Note there is no tax for having foreign accounts or assets, but there are harsh penalties for failing to report them on FBAR or 8938 as required. And any income on them, like interest or dividends, is usually taxable.
I recommend you look at (and probably download) IRS' specific publication on this topic, pub 54, Tax Guide for U.S. Citizens and Resident Aliens Abroad so you don't get unpleasantly surprised next year. Unfortunately as far as I can see it doesn't address capital gains, your actual question, except to say they aren't earned income which we already knew. The question is whether US or Ireland gets 'first crack', and if you were not a US citizen (or LPR) then capital gains are sourced to your location i.e. Ireland, but I don't know for a citizen. If I have time to look at the treaty later I will update.