Base Singer
You will need to arrange cover through an Irish Insurer or broker, as you are only a temporary resident here while your are studying.
What cover are your looking for exactly? Is Travel Insurance the right type of cover? You may be better off taking out Student Personal Possessions Insurance to cover your possessions as Travel Insurance is limited. Do a google search and you will note many Insurers provide this.
In regard to health cover, you need to arrange for a European Health Insurance Card in Ireland, so you can access the NHS. I believe UK and Ireland have a receiprocal health service arrangement anyway, but the card may be helpful.
Huckster