TGV is probably a bit OTT as it would require completely new lines. 125mph/200kph for Cork-Dublin and Dublin-Belfast should be the focus as that is achievable by upgrade of existing lines. That would also benefit Dublin-Kerry/Limerick/Galway/Mayo/Waterford.
Once done, look at Portarlington to Athlone. Get those sections up to 125mph and coaches (and to a lesser extent car, which always benefits from immediate departure) are a much less attractive option.
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