You must by Hungarian law pay tax on rental income in Hungary.
If you are a tax resident in Ireland, you must also pay tax on worldwide income in Ireland.
You have to pay tax in both countries.
However, there is a double taxation treaty between Hungary and Ireland.
Any tax you pay in Hungary is deducted from your tax liability in Ireland.
In reality, you probably wont have to pay much tax in Ireland, because the tax you will have to pay in Hungary is high.
It's over 20% of the gross rental income.
In Ireland you only pay tax on the profit on the Hunarian property i.e the gross rental - costs.
The Hungarian tax would normally be greater than your Irish tax liability, therefore your tax liability in Ireland on the venture would likely be very small.
For example (the percentages are for illustration only)
Gross rent = 10'000
profit on venture = 3000
Hungarian tax liability = 10'000 * 20% = 2000
Irish tax liability = 3000 * 40% = 1200
Your Irish tax liability would be 1200 - 2000 = zero