There is a student railcard, although this has currently been melded into a young person's discount for under-23s as a notionally temporary measure to promote public transport use post-COVID.
The discount being applied to all under-23s regardless of student status, and the 50% discount level on State-funded (PSO) services are both officially permanent as per the announcement in Budget 2022 - the only temporary part is the State-subsidised 50% fare on private bus operators' services (which is supposedly a cost-of-living measure aimed at students who commute to/from college). The scheme for private bus operators was a poorly thought out decision borne from needing to be seen to be doing something anyway - it's been massively abused, with several entirely student-aimed operators doubling their fares immediately before joining (so instead of getting a €10 fare from the student, they now get €20 - €10 paid by the student and €10 paid by the State); and part time students over 23 were thrown under the bus [pardon the pun] with a massive price increase overnight (they were previously eligible for the operators own student fares, but now pay full adult fare as the State-subsidised scheme is not available to part time students, and every operator bar one who joined the State scheme revoked their own student fares on joining)
It is, of course, not a Railcard in the UK sense - aside from being valid on buses, and being de facto free (€5 deposit + €5 minimum travel credit top-up - both refundable on expiry if not used), it is not even mandatory for the discount (except for private bus operators, who are required to record card numbers to prevent them abusing the subsidy) - with Irish Rail accepting any student card, full or part time, from anywhere in the world; and PSO buses accepting any Republic of Ireland student card, full or part time (and in practice Northern Ireland and UK student cards too).
As mentioned further up, residents aged 66 and up get free travel, as do recipients of certain disability benefits. Depending on the specific circumstances, a spouse or equivalent, or a carer (which may be anyone aged 16 and up) may accompany them.
In addition, residents of Northern Ireland aged 65 or over travel free within the Republic of Ireland; while Blind and War Disabled residents of Northern Ireland can travel cross-border but not wholly within the Republic. Reciprocally, residents of the Republic of Ireland aged 66 or over can travel free in Northern Ireland; while under 66s with free travel can travel cross-border but not wholly within Northern Ireland. (Although in practice, I know that many who are only entitled to cross-border travel abuse break of journey rules and the availability of anywhere-to-anywhere through ticketing to make journeys wholly within the other jurisdiction - for example, I'd imagine the number of cross-border free train tickets issued from Londonderry to Dundalk exceeds by several orders of magnitude the number of regular tickets sold for that journey)
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