Anglo-Irish relations will remain challenging regardless of whether the next UK prime minister is Rishi Sunak or Liz Truss, according to Fine Gael's spokesperson on European Affairs.
The former chancellor and the foreign secretary finished in the top two places after five rounds of voting by Tory MPs, with Penny Mordaunt eliminated from the race after a bitter contest in Westminster.
Mr Sunak and Ms Truss will now face a campaign to win the votes of Tory members, with the result of the contest announced on September 5th. The winner is expected to replace Boris Johnson as UK prime minister the following day.
Dublin Rathdown TD Neale Richmond told BreakingNews.ie: "I'm not exactly excited about either candidate, Sunak is a career Brexiteer and Liz Truss is the person behind the protocol-busting piece of legislation that is going through the House of Commons."
Both Mr Sunak and Ms Truss were heavily involved in Mr Johnson's government, so Mr Richmond does not expect significant changes in their approach to Northern Ireland.
However, he said they may take it more seriously.
"What's going to change with either of them becoming prime minister is the personality, you could argue that both are more serious politicians than Boris Johnson. Johnson, for want of a better word, was often described as 'colourful'.
"You'd hope that both would apply themselves when it comes to Anglo-Irish matters. Issues with the EU and UK, issues with the protocol, issues in relation to legacy, issues in relation to immigration in terms of the Borders Bill.
"We're at a really difficult time in relations and now is a time we need a serious British prime minister who will lead a government to take their responsibilities seriously."
Because of the difficulties in Anglo-Irish relations, and the UK's relationship with the EU, he said the Tory leadership contest will be important for both Irish and EU politics.
He also said there will be an opportunity for a "reset".
"There is an opportunity for a reset, for a new prime minister to take things in a manner which is a lot more collegiate. The UK and EU have cooperated quite well in response to Ukraine and many other matters, but there are many areas that need scope for a more realistic approach.
"Sadly, I don't think that one candidate more than another presents us a great shining light in this regard. I think the internal debates have been quite dispiriting in terms of some of the rhetoric that's come out, the blatant falsities that have come out from certain candidates - not necessarily these two. We're going to have another difficult couple of months while the Conservative Party decide their new leader and UK prime minister. There will be worrying references to Brexit and the protocol, worrying and potentially ignorant as well."
Ms Truss is responsible for the controversial Northern Ireland Protocol Bill, which looks to ditch large parts of the Brexit agreement agreed by the UK government.
While the Bill has cleared the House of Commons, Mr Richmond feels it will struggle to get through the House of Lords, and he expressed hope of a more "realistic" proposal to break the deadlock.
Liz Truss as foreign secretary kind of absconded from negotiations since February.
"The legislation itself is difficult, it breaks international law. We want a negotiated solution to the difficulties that are being caused post Brexit that can be solved within the protocol, but we need it to be done with someone who will take their job seriously, take the job of restoring Anglo-Irish relations seriously.
"Liz Truss as foreign secretary kind of absconded from negotiations since February.
"There's always opportunity for the British government to amend or review this legislation, it's going to get a kicking in the House of Lords, there isn't a majority to pass it in the House of Lords, it could be blocked or delayed.
"Our role is to continuously push it and keep it on the agenda, not to let it slip off and to do that both in a direct way with the British government and our European partners."
Northern Ireland has barely been mentioned in the Tory leadership debates so far, and Mr Richmond said this has been a "consistent theme of this British government, the priorities change every morning, they've been racked with scandal".
He added: "There's been a short-term approach in certain areas and unfortunately that will be heightened with internal policy and political debates if they do refer to Northern Ireland or the EU more widely, it's not going to be in a positive or proactive manner.
"At the end of the day, the UK is a really important partner of Ireland and the EU, co-guarantors of the Good Friday Agreement, we have a responsibility to work with whoever becomes prime minister. It's going to stay challenging with whichever of these individuals take the job, I just hope it won't be as challenging as it has been with Boris Johnson.
"These are two people who were more than happy to be a part of Boris Johnson's Cabinet, and to attack in accordance with the many moves in the last few months that have been so detrimental to Anglo-Irish relations."
Mr Richmond said he would "like to be optimistic", however, "unfortunately it will be a continuation to a large extent of what we've been experiencing so far and that hasn't been a good place, so we need to see a lot of effort from ourselves, our partners in the UK, and many others to try to make this work as best possible, we can't ignore it, it's going to be impactful".
"This Conservative leadership election isn't going to facilitate a return of Stormont any quicker. It's not going to allow for a betterment of relations in the short term, it's not going to allow for meaningful negotiation on how to implement the protocol in a better manner.
"What we have with this leadership is a period of stasis, you just have to hope that period of stasis can be followed by an opportunity for a reset with a new prime minister, potentially new ministers in key departments."
Mr Richmond feels the Government may have to act as "fact-checkers" for any outlandish claims about the Northern Ireland Protocol in the remaining leadership debates.
"Where required we have to correct the falsities and nonsense spouted by the leadership candidates or their campaign teams and supporters.
"Simon Clarke, the chief secretary of the treasury going out and talking about all these made up Brexit benefits, Suella Braverman misleading people on the impact of the protocol in Northern Ireland, these are the areas where we have a responsibility to speak truth to power and be that important fact-checker in the argument, and as a Government to keep pressing the agenda and keeping communication lines open."
While he doesn't expect much policy change in relation to the protocol, he feels it is the role of the Government and EU partners to keep highlighting the issues in relation to Britain's current approach.
"It's a massive responsibility for the Government to really continue to push and to force the issue with the new British government about the importance of restoring the institutions in the North. Making the protocol work and having a level of engagement that just hasn't been where it should be in the last couple of months between the British and Irish governments as well as our partners in the EU.
"If anything the heavy lifting in this area is going to have to be done by the Irish Government because sadly we've had a British government that has been too disinterested in its responsibilities for too long."