Thank you for your reply.
So the market value for the valuation is also the date of death value and not the sold price as I thought. The two different types of tax related to the same event, (ie finalising the deceased's affairs and distributing the inheritance) are handled separately.
The tax due on the increased value of the house is CGT and that calculation uses the sold value less the value at date of death less any costs / expenses. This is the responsibility of the executor and if tax is due, the executor has to pay Revenue and file a tax return on behalf of the estate. When the executor finalises the estate, the beneficiaries are paid their inheritance.
Any tax due on the inheritance is CAT and that calculation uses the valuation date and the relevant thresholds. This is the responsibility of individual beneficiaries.