Whether a new lender is interested is all down to return on equity, with the amount of equity a bank lender must put up being driven by bad debts of which enforceability of security is a major factor.
There are big fixed costs associated with mortgage provision - underwriting, a branch network,regulatory, etc
There are very little fixed costs to start originating and servicing mortgages. A branch network is the very last thing that a new lender would think about setting up. Almost everything can be outsourced for a set percentage of the balances written / serviced. There are some fixed costs, but they aren't material.
In terms of market size, there are over 700k mortgages with an outstanding balance of just shy of 100bn. Just over 9bn of new lending was written last year, with 10bn expected this year. The market is big enough for a new lender if they saw the margins worthwhile for the risk they have to take on. Yes, it'd take a while to build up a worthwhile book size, but a new entrant gaining 20% share would be writing 2bn per year.
New Zealand - a market pretty similar to Ireland - basically has four banks of any consequence and foreign banks aren't interested in market entry as its so small
It might be a small market, but there are at least a dozen lenders offering mortgages in the main cities. I know one or two are subsidiaries of others, but there's a lot more competition there compared to here.