You can lodge an Australian cheque to your Bank of Ireland account. You can do this with a cashier in any branch and it can take up to six weeks to clear in your account and will be subject to a lot of fees etc. As an alternative, perhaps you could get the superannuation cheque cancelled, then open up an AUD borderless bank account with Transferwise - then get the superannuation payment paid electronically to your Transferwise borderless account from where you can then instantly transfer it to your Irish EURO bank account saving you a lot on fees and no waiting time. I have a Transferwise borderless AUD account and find it great for receiving AUD payments and transferring to Euro. Good luck with sorting it out.