Irish premier Leo Varadkar has said that the new EU-UK trade deal for Northern Ireland will not be renegotiated, but added that Brexit “will never just be done”.

The Taoiseach also said he is working with Prime Minister Rishi Sunak to attempt to restore the powersharing institutions after Northern Ireland’s local elections next month.

In a push to revive the Stormont Assembly and executive, a new trade agreement was struck by the EU and UK in February that sought to amend the post-Brexit protocol and resolve the concerns about red tape raised by Northern Ireland businesses and unionists.

Although the British parliament and EU have formally signed off on the Windsor Framework deal, the DUP and former prime ministers Boris Johnson and Liz Truss have voted against a key element of it.

The DUP has made clear its ongoing boycott of the powersharing institutions will continue until it secures further assurances over its concerns around sovereignty and the application of EU law in Northern Ireland.

During a live interview at Bloomberg’s New Economy Gateway Europe event in Dublin, Mr Varadkar said that he believes the Windsor Framework resolves the relationship between the UK and EU.

“It has now been agreed between the EU and the UK, nobody is calling for it to be opened or renegotiated, not even the DUP,” he said on Thursday.

“The issues they raise are bilateral with the UK Government. So I do think it gives us a settled trading relationship for Northern Ireland.

“Now we need to focus on getting institutions back up and running, but that won’t involve reopening the Windsor Framework.”

He also said that he hoped for a closer trade relationship between the UK and the EU in future years, but added that the prospect of the UK rejoining the bloc was “remote”.

“What I would say though, is that none of these things are necessarily the final word with the UK’s trading relationship with the EU,” he said.

“We know that in the next few months, they are going to start their checks on imports from the EU.

“That’s going to affect us, and anyone who trades with the UK. Brexit will never just be done, it will require constant negotiations and alterations to the relationship.

“The beautiful thing about the single market is that you don’t need to worry about any of that, you all have the same rules.

“The relationship with the UK is going to be more like the relationships we have with Switzerland or other third countries like Norway, where agreements have to be amended from time to time.

“One thing I would still hope for in the future, and it’s not impossible in my view, is that a future British government – maybe not the next one, maybe not the one after that – will seek a closer relationship with the European Union again.

“That might not be rejoining, I think that’s a remote prospect, but it might involve a revision of the Trade Cooperation Agreement to have a closer relationship, and that’s something that the door will always be open to.”

He said he hoped pressure on DUP leader Sir Jeffrey Donaldson would have a positive effect.

“But I don’t think the DUP will be browbeaten or bullied into doing anything. They will make their decisions based on what they think is right, hopefully, what is right for Northern Ireland, Ireland, and the UK, and not what is just right for them as a political party.

“And they have set up a group under Peter Robinson that is advising them on what the next step forward should be.

“There are local elections in May, but Prime Minister Sunak and I will be working towards a window after the local elections to try and get the institutions stood up.

“I’m very keen to talk to the five major parties about that.

“Let’s not forget there are five major parties in Northern Ireland. The DUP is important because it is the biggest party representing the unionist community. But it is not the only one. It has 20% of the vote and we shouldn’t forget that.

“And I do think that if the new Executive is going to be set up, it will need help from the two governments – political help, financial help, and we’re up for that.”

He said that the only plan is to “stand up for the institutions” and said that he didn’t believe that anyone thought direct rule from Westminster was viable.

“And nobody thinks that a new set of elections will change things. So Plan A is the only plan at the moment,” he said.