Tax Credits:
As a non resident you will be entitled to the proportion of tax credits that your assessable Irish income bears to your total worldwide income. Therefore if your foreign income is high, your tax credits will be low.
Tax Bands:
You will get the normal tax bands, and therefore based on above expect to pay 20% of your net profits (income less tax deductable expenses)
Mortgage Interest:
You will only receive a credit of the interest you pay on your mortgage if you are registered with the PRTB.
Tax Return:
As a non-resident landlord you will need to file a return every year.
Agent:
Unless you appoint an agent to act on your behalf (an Irish resident friend or family member will do) the tenant is obliged to withhold tax of 20% of the gross rents and pay this over to the Revenue. To remain tax compliant I would suggest that you appoint an agent. If you do so your agent will receive a new PPS number, and will file tax returns on your behalf as "XXX, agent for XXX"