Why is the Republic Of Ireland so slow in giving out the vaccine compared to Northern Ireland they are miles behind......?

Because the ROI has had to wait for a supply from the EU who were very slow to order/pay for vaccines and slow to deliver, where as NI is part of the UK and the UK ordered/paid for and delivered far quicker...even though the EU tried to block NI getting their vaccines from the UK

Because they're two different countries, with different government, systems, and choices.
Also one is part of the EU, and one is part of the UK.

I'm a nurse currently giving people their vaccine jabs in the RoI, so here's my tuppence worth ... 

The UK were very efficient in terms of their provisioning of the AstraZeneca vaccine. They didn't just pay for supplies - the government helped in terms of the supply chain, approving various companies and facilities for supplying elements of the vaccine, and so on.

The EU negotiated a great deal. We'll pay less per vaccine than the UK will. And the Eurocrats congratulated themselves for that. But they didn't do the the actual 'on the ground' work to facilitate the rollout of vaccines. They took a much more consumer vs supplier approach which was short-sighted. And now they're scrambling to catch up.

Having said that though, it's now pretty clear that the UK signed a deal that amounted to vaccine nationalism. European plants supplied the UK with vaccines but not the other way around. AstraZeneca made it very clear that they were honouring their UK commitments at the same time as reducing supply to the EU. And before the UK implodes in a black hole of smugness, at every step their government has been slow to respond to Covid so they are eager to deflect from failings for a year with recent vaccination successes.

But basically it comes down to supply. If I don't have vaccines I can't inject people. The question the UK needs to ask is whether it is morally and ethically correct to vaccinate low risk members of their population while neighbouring nations don't have the supplies to vaccinate our vulnerable.

Because per head of population the rates were much lower in the republic so no pannick