Income tax: You'll be liable to income tax in Ireland on the rental income from your Irish property.
If the rent is paid directly to you, because you will be non-resident the tenant will be obliged to withold 20% of the gross rent and remit it to the Revenue Commissioners. You then engage with the Revenue Commissioners to finalise your liability and you get credit for the 20% remitted by the tenant. If your liablity is less than that you can get a refund.
You can avoid this by appointing an agent who is resident in Ireland to receive the rent on your behalf, and I would reccommend this — you really don't want to be involving your tenant in your tax administration. (Your tenant won't want this either.) The agent could be a professional — an estate agent, for example, who does this for a fee as part of a property management service — or it could be an obliging family member. The only requirement is that they be resident in Ireland.
You may, of course, also be liable to tax on the Irish rental income in the country in which you are resident — that depends on the laws of that country. If you are, there may be a Double Taxation Agreement between Ireland and that country which gives you relief from paying two lots of income tax on the same income. Obviously, all that depends on what country you are moving to.
Capital gains tax: While you're away, the property will not be your principal private residence. When you eventually sell or dispose of the property, it may not be wholly exempt from capital gains tax. If, say, you have owned it for 20 years and you were abroad for 3 years of that, then 17/20ths of any gain will be exempt from CGT and 3/20ths will be subject to CGT.
It's actually a bit more complicated than that, since there are some reliefs available if you go abroad in connection with your employment. Plus, if you sell the house while still abroad, or within 12 months of returning, for the last 12 months of the period of ownership it will be treated as having been your principal private residence even though it wasn't. So look into this before you make any definite commitments about going abroad, and see if you can arrange matters to minimise or eliminate any CGT liability.
