First of all I take it that your tenants are deducting tax from the rent before forwarding it on to you (even if the rent is being paid into an irish bank account) unless you have appointed an agent in ireland. If not they could become liable for any shortfall in tax that you have to pay to the Irish authorities.
You are making annual tax returns to Irish revenue in respect of the property and perhaps Australian Revenue (you need to check this out)
You may not have any liability to Irish revenue but you could have to Australian revenue if they calculate rental income the same way as Ireland does i.e. on worldwide income
In the same position here. Irish citizen, resident in Australia and having a property in Ireland. While I am not a tax adviser I have taken lots of advice and the information is general confusing but this is what I got out of it:
1. Australian tax laws apply to your foreign income (i.e. from Irish rent)
2. When refinancing any property (whether its in Ireland or Australia) then the interest on borrowings are only offsetable against taxable income if the purpose of the funds is to further invest and generate income (i.e. cant use it to buy a bigger house for yourself in Australia)
3. Your maximum amount of foreign interest deductions that you can offset against tax is limited by "thin capitalisation" rules. Which effectively puts a cap on how leveraged you can be (from a tax benefit point of view)
4. Negative gearing in Australia is not very effective on the irish property. This is because losses associated with the foreign property are only allowable against income from that source (i.e. cant run up a loss and get your australian income to cover it).