Upvote:-3
Your question concerns entering the USA, and this has been answered already. However the premise of the question contains a misconception regarding your ability to travel in the EU - which is what gave rise to your consideration of using an Irish passport in the first place.
Quote: "considering the upcoming Brexit uncertainty regarding access to the EU for British citizens"...
This is a symptom of the tendency for the media to peddle scare stories. I can 100% guarantee you that even in a "no deal" scenario, there will be nothing to prevent you travelling to any EU country for business purposes.
The EU right to free movement simply means that EU citizens can live and work in each other's countries without having to apply for permission. Removing these rights doesn't mean that people travelling on holiday or business won't be allowed to do so. Even in the worst case scenario, it just means you'd have to queue up and present your passport to an Immigration Officer (the same as you do now, since the UK is not in Schengen); but instead of being simply waved through, the officer will have the right to ask you how long you intend to stay and why you're visiting.
This is exactly the same as when any other non-visa, non-EU citizen visits. When, for example, an American or Japanese citizen flies into Berlin on business, they present themselves to the Immigration Officer as usual, and are granted entry to the country for the purpose of that visit.
You don't require free movement rights simply to visit other countries. Brexit won't change that - even in the worst-case scenario.
Source: I write as a former Immigration Officer.
Upvote:12
There are no issues with obtaining an ESTA with a different citizenship than you've used for a previous ESTA.
As a part of the ESTA application you will be asked if you have a passport for any other countries, and whether you hold any other citizenship - obviously in this case you will need to declare your UK citizenship/passport as a part of the application.