I'm afraid the answer is yes. As a UK resident with earnings that arise outside the UK you are obliged to complete a return of that income to the Inland Revenue in the UK under self-assessment rules. You should be given a credit or relief in respect of any Irish income tax you are paying because of the double taxation agreement between the Republic of Ireland (ROI) and the UK. There may or may not be a balance of income tax to pay to Revenue in the UK.

Depending on the number of years you have worked in the UK and in ROI you may qualify for a State pension from either the UK, the Republic, or both. European social security rules allow contributions made in different member states to be combined on a pro-rata basis so that contributions in the Republic could enhance the rate of a northern-UK pension and vice versa.