Notice 741A, section 7, details the "land related services" exception to the general place of supply rules. But if it's a B2B supply, the place of supply would be the ROI regardless of whether it was a land related service or fell under the general B2B rule. Currently, you would not need to register for VAT in the ROI. You would invoice without VAT, and your customer would be liable to operate the reverse charge - meaning that they would calculate the VAT due and pay it over to the ROI tax authorities. They would then also reclaim that VAT, to the extent that they would have been able to if the supply had been made by a ROI company.
Please note that my opinion above is based on the current position. It does not take account of any changes which may arise following the end of the Brexit transition period on 31/12/2020.