Housing
Enda Kenny said the housing crisis was one of the most pressing issues facing his government, and that remains the case for the administration led by Leo Varadkar.
Simon Coveney has used the last year to launch a number of plans to tackle the issue, such as the Action Plan for Housing.
Supply has yet to catch up with demand, although government insiders say building activity is increasing.
The most immediate issue, however, is Mr Coveney’s self-imposed deadline of July for having no families living in hotels and B&Bs. That is unlikely to be met.
Brexit
During the Fine Gael leadership campaign, Leo Varadkar praised the approach of Mr Kenny in tackling Brexit.
He also said he would seek to keep Northern Ireland in the European single market, although this is likely to be met with resistance from the new Westminster power brokers, the Democratic Unionist Party (DUP).
Mr Varadkar says he has a good working relationship with DUP leader Arlene Foster and this is likely to be crucial as Foster seeks to soften the Brexit policy of Theresa May's Tory government.
Keeping the UK in the Customs Union, as the DUP seems to favour, is probably a more achievable aim.
Public Sector Pay Agreement
The recent pay deal has largely taken the thorny issue of public sector pay off the table, but individual unions still have to ballot on the agreement.
In particularly, those who feel they have been hit because of their fast accruing pensions – such as Garda representative associations – have the potential to cause trouble. The new Cabinet will still have to be on its toes on the issue of public sector pay.
Garda reform
Reform of An Garda Síochána itself has dogged both Fine Gael led governments in recent years, and the previous Cabinet decided against seeking to remove Garda Commissioner Nóirín O'Sullivan from her position.
Ms O'Sullivan's position is likely to come into question again, however, as the PAC continues its investigations into the Garda training college in Templemore and the Charleton Commission which is dealing with issues raised by Garda whistleblowers proceeds with its work.
Mr Varadkar has thus far expressed confidence in Ms O’Sullivan and his Minister for Justice will have to oversee the new Commission on the Future of Policing in Ireland, due to complete its work within 18 months.
The new Cabinet will likely have to decide soon whether to stick by Ms O’Sullivan.
Northern Ireland
The talks to establish a new executive in Northern Ireland have taken on an added urgency because of the new influence wielded by the DUP in Westminster, with Sinn Féin now saying the institutions can be up and running in days, if the will is there.
With the impartiality of the UK government as an honest broker now in question because of its reliance on DUP support, Mr Varadkar and his Minister for Foreign Affairs will have to strike a delicate balance.
Fine Gael has a reputation of being disinterested in Northern Irish affairs and Mr Varadkar has made his distaste for Sinn Féin well known. But, as co-guarantors of the Good Friday Agreement, his government must be concerned over the DUP influencing the British government and its effect on nationalism.
Infrastructural spending
Mr Varadkar has signalled he wants to significantly increase infrastructural spending to catch up on years of under-investment during the crash.
He has said he wants to revise the debt level to 55 per cent of GDP from 45 per cent and use the leeway for greater infrastructural spending. He will also face demands to use the sale of AIB shares to further boost infrastructural spending and will need to juggle competing political demands of where in the country is deserving of new projects.