if a person moved to the UK and sets up a limited company and pays themselves dividends are those dividends still liable to irish tax until the person is no longer "ordinarily resident" in ireland? Or are they exempt as they can considered as income from caryring out a trade or profession?
Taken from Revenue's Guide Res1: How will sources of foreign income other than employment income be treated when I am non-resident?
For any tax year during which you are non-resident but remain ordinarily resident (see What is "Ordinary Residence"? ) your foreign sourced income (excluding income from an employment, a trade or profession, the duties of which are not exercised in the State) will remain chargeable to Irish tax unless such income does not exceed €3,810 for that tax year. If the income exceeds €3,810 the total amount (not just the excess over €3,810) becomes taxable. However, the provisions of a Double Taxation Agreement between the State and the country in which you are resident may affect the taxation of such income.
Essentially, if the dividend income in the UK exceeds €3,810 in the calendar (and bear in mind that the UK tax year runs to 5th April unlike here) then you will be taxable here on it, with a credit available for tax already borne on the same source in the UK. Calculating this credit would probably be a bit convoluted.