I will summarise events from September 1913 to November 1917 because I have written about them in detail here:
https://www.alternatehistory.com/discussion/showthread.php?t=120658 .
In September 1913 Sir Horace Plunkett announces that he will call a convention which will discuss all options for the future of Ireland within the British Empire.
The Irish Convention starts its deliberations in October 1913 under the chairmanship of Lord Dunraven. It hears evidence from a wide range of opinion: political ranging from Ulster Unionist through mainstream nationalist to Sinn Fein to socialist; from churches and religious bodies; from women's groups; from trade unions; from business groups and professional organisations; from academics, lawyers and anyone else with relevant expertise.
The Majority Report of the Convention is published on 8th July 1914. It recommends the establishment of a two-chamber legislature for Ireland elected by proportional representation. It would have power over all areas which are currently the responsibility of the Chief Secretary for Ireland. There would be constitutional safeguards for the Protestant minority. Irish representation would continue at Westminster.
The First Minority Report by Sinn Fein and its allies calls for an independent Ireland. The Second Minority Report by the Ulster Unionists proposes that there is no change to the status quo. However if Home Rule is ever implemented then Ulster should have the right to opt out.
Plunkett announces that the Majority Report has his full support. Balfour says that it offers a constructive way forward and that he will give it his careful consideration.
The events leading up to the First World War and the declaration of war by Britain on the Central Powers happens as in OTL. Balfour appoints Lord Kitchener as Secretary of War on 5 August 1914.
The Government of Ireland Bill (popularly, though unofficially called the Irish Home Rule Bill) is published in February 1915. It provides for the establishment of a two-chamber Irish Legislature comprising a National Assembly of 150 members and a Senate of 50 members, both elected by Proportional Representation. 60 members of the National Assembly and 25 members of the Senate would be elected by the nine historic counties of Ulster: Antrim, Armagh, Cavan, Donegal, Down, Fermanagh, Londonderry, Mionaghan and Tyrone. The Senate would have the power to veto legislation from the Assembly provided that the marity for the veto is at least two-thirds of the senators voting.
Bonar Law, the Colonial Secretary, and Sir Edward Carson, the Attorney-General, both resign from the government in opposition to the bill. It receives its second reading with the votes of Liberal, Irish Nationalist and Labour MPs after a three day debate in February 1915. However only 104 Conservative MPs vote for it, compared to 187 who vote against it.
In the Committee stage amendments are passed which give women ratepayers (local property tax) payers and the wives of male rate payers, the right to vote for the Irish Legislature; and that the Legislature will be called a Parliament. Amendments to include all or part of Ulster are defeated.
It receives its third reading in July 1915, again with only a minority of Conservatives voting for it. In November 1915 it is rejected by the House of Lords by a majority of 293 votes to 93 votes. Balfour says that he will not reintroduce the bill this session.
In spite of strong pressure from right-wing Conservatives, and Liberals such as Lloyd George and Churchill and their allies, the Balfour government does not enter into a coalition government of National Unity with the Liberal and Labour Parties. A sustained attack for the introduction of conscription by the same groups in the Conservative and Liberal Parties is resisted by the government.