Under the current rules can an Irish person double vaccinated gain a 28 day visa on arrival once he has done the 7 day quarantine can he then gain an extension of an additional 30 or 60 days. Thanks for any advice.

Kind of, he can arrive visa exempt (visa on arrival is a different beast and not relevant to an Irishman) and get stamped in for 30 days. Then entitled to 1 x 30 day extension. By then who knows if the 60 day Covid extension will still be available. Unless flying in the next 12 days likely to just have 1 day max "quarantine".