The short answer is yes but you need to make sure you have the correct documents. There are 2 main banks in Ireland and these are the ones that a UK citizen moving to Ireland from the UK would look to bank with:
Allied Irish Bank
Bank of Ireland
To get a bank account in Ireland you will need to prove you have a residential address and a lease or tenancy agreement is not sufficient. Normally, you need a PPS number before you can get a bank account in Ireland.
You can make an appointment to meet with the bank in person. However, Bank of Ireland has an online portal that allows you to open an account if you have:
Irish proof of address
Our experience is that you can set up a personal bank account with Bank of Ireland in about 48 hours using their online portal.
Another good option for personal banking in Ireland is Revolut. Revolut has over 2 million customers in Ireland and the phrase "Revolut me" has become part of the lingo, especially with younger people.