I wouldn't fully close a bank account in the UK until a minimum of one year has passed in case payments or outgoings that you've forgotton about are fully dealt with. For example a UK revenue refund, insurance refunds etc.
Suggest you give you current employer and pension provider (if any) a new Irish address for any future contacts
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Do you have an Individual Saving Account (ISA)? it might be worth thinking about leaving it in place if you don't need the money right now. You will always be free from UK tax from gains on this account, so if you ever go back that'll be a thing. I don't think there is an equivalent in Ireland, AAM peps is that right?
"You have to be an UK resident to hold an ISA.". Are you sure about that? My understanding is you have to be resident to CONTRIBUTE to ISA but not to maintain it.
This is from www.gov.uk
6. If you move abroad or die
If you move abroad
If you open an Individual Savings Account (ISA) in the UK and then move abroad, you can’t put money into it after you move (unless you’re a Crown employee working overseas or their spouse or civil partner).
However, you can keep your ISA open and you’ll still get UK tax relief on money and investments held in it.