What exactly are you trying to do? Switch lender, or release equity?
It's a rental, so it's a buy to let. That's how banks will treat it.
Banks will lend to non residents for investment, but the monthly rent usually has to be at least 1.2 times a stressed Mortgage payment (i.e. interest rate increased by 2%).
AIB will consider this, but they will treat it as a buy to let (which it is). I don't know they're exact criteria.
If your income is non Euro, it's complicated as it's treated as a foreign currency loan under the Mortgage Credit Directive. Having the rent being more than the stressed Mortgage repayment gets around that.