As far as my knowledge goes:
Assuming you have spent more than 183 days in Ireland for 2020, you are tax resident in Ireland in 2020, and assuming you are UK domiciled, then you are taxed on Irish source income and foreign income remitted to Ireland.
As a non-Irish domiciled person, you can avail of the 'Remittance Basis of Taxation'.
Thus, your UK rental income should fall outside the charge to tax in Ireland provided none of the funds are remitted to Ireland.
If you are not remitting any foreign rental income to Ireland, then there is nothing to declare under Schedule D Case III for income tax.