This question is fatally flawed, the 1916 rising is a separate event from the war of independence, though very closely related, the rising lasted only lasted the week of Easter and involved around 18,000 combatants all together (mostly British troops), which was at best a brief detour from the struggle on the western front. Almost all of the leaders of the rising were killed in the aftermath, Eamon De Valera being the highest profile survivor, and most of the rank and file revolutionaries were interned in Britain. Just under 500 people are recorded to have died in the Rising, but Ireland remained peaceful for the rest of World War 1, however the Rising obviously had a major impact on Irish politics, initially regular Irish people, especially in Dublin, were bewildered and often furious about this unexpected rebellion and resulting destruction, but the British government made the mistake of executing the leaders of uprising and drawing the executions out over a long period of time, this seems to have caused public opinion to become more sympathetic to those involved in the Rising as martyrs for the cause of Irish nationalism. The British also associated the Rising with the political party Sinn Fein, even though their leadership had nothing to do with it, and cracked down on them, arresting their leader, Arthur Griffith, soon after. As a result Sinn Fein became a locus of political organisation in favor of the aims of the Rising almost by accident.

As time went on the British seemed to have realized that their current approach wasn't productive, stopped the executions and started releasing prisoners associated with the rising, but by this point the damage was done, support for Sinn Fein started to grow rapidly among nationalist minded Irish people who started abandoning the Irish Parliamentary Party, which previously dominated Irish nationalist politics. The IPP was more moderate than Sinn Fein and had fought for decades for a dissolved parliament in Ireland rather than full on independence. John Redmond. the leader of the IPP had actually managed to achieve this in 1912, but the prospect of home rule for Ireland was extremly controversial among unionists in both Britain and Ireland, so the project was delayed as long as possible to avoid civil war, it was then interrupted by World War 1 and shelved until the war was concluded (some think that this so called 'Ulster Crisis' might have played a key role in German decision making that caused them to invade Belgium since they assumed the British were going to be too distracted by internal political struggles related to Irish Home Rule to respond). Redmond had supported the war in part because he assumed this display of loyalty would ingratiate the Irish nationalists to the British, but this was always a controversial move in Ireland since a lot of the population was understandably skeptical about fighting Britain's wars.

The delay in initiating Home Rule as well as the increasing unpopularity of war and intense feelings brought to the fore by the Rising and it's aftermath started to eat away at the IPP, even though Redmond was actually one of the most important figures arguing for clemency for the revolters. The final straw came with the German spring offensive in 1918, up until then the British had not introduced conscription to Ireland since it would have been a political nuke in the country, but panicking at the prospect of the Western front collapsing and the Germans achieving victory the British government clumsily attempted to push it through to shore up their faltering manpower. This caused furious opposition and radicalization in Ireland, and as luck would have it John Redmond died just in time to let Sinn Fein take the initiative in this opposition and leave the IPP in the dust. Conscription of course never went through, and this was perceived as a major victory for Sinn Fein, subsequently the British attempted to crack down on Sinn Fein again, which predictably had the opposite to the intended effect when Arthur Griffith and others were thrown in jail as German agents, just making the Irish public more pro-Sinn Fein and anti British. This all lead to the general election of 1918, probably the most important in Irish history where Sinn Fein, previously holding 6 seats, completely annihilated the IPP and took 73 of the available seats in the country, out of 105 (most of the rest went to northern unionists). Mere Home Rule was no longer an acceptable objective for Sinn Fein compared to the IPP and, especially in the face of the end of WW1, the rhetoric of national self determination all over Europe and the ever increasing radicalization of Irish society since 1916 crisis became inevitable. Sinn Fein refused to physically go to Westminster to take their seats (they still do this to this day) and instead began an illegal (in the eyes of the British) government in Dublin called the Dail, which declared an Irish Republic in the same vein as the leaders of 1916. The war of independence is generally agreed to have started soon after, in January 1919 with the Soloheadbeg ambush as the IRA attacked police presence in the country to undermine British authority.

Hope that helps.

u/Khwarezm has given two excellent answers, I have only a few points to add relating to the impact of the 1916 Rising on British effectiveness during the war (as he points out the War of Independence doesn't begin until 1919).

John Redmond, the leader of the Irish Parliamentary Party, had agreed to the suspension of Home Rule for the duration of the war and called on the Irish Volunteers to "go as far as the firing line extends" (enlist and fight in the war). Of the 150,000 or so members who split from the Irish Volunteers to form the pro-Redmond National Volunteers only about 24,000 answered this call. Many Irish fought in the First World War but it was never popular to begin with. Increased agricultural prices meant many farmers were reluctant to allow their sons to fight for example.

A short war had been promised but by 1916 the Home Rule bill had been delayed multiple times. The Ulster Volunteer Force, which had threatened civil war to resist Home Rule, was allowed form its own division and have its own officers, both of which was denied to the National Volunteers. The Catholic Church had came out against the war early in 1916 and reports on heavy Irish losses at Gallipoli also made the War unpopular in Ireland.

This is all to point out that the War was already unpopular before the 1916 Rising, but following the executions and a number of British atrocities in Dublin, recruiting levels plummeted in Ireland. Ireland was made exempt from conscription when it was introduced in March due to fears of unrest and the Rising had a further effect on recruiting levels in the country. Following the German Spring Offensive in March 1918 Britain introduced conscription but was never able to enforce it. The Lord Lieutenant, Lord French, tried to get 50,000 volunteer recruits from Ireland by October but was only able to secure about 8,000. Throughout the year recruitment levels did rise but remained well below what was needed to replace casualties in Irish regiments and many of these had to be combined together.

The Rising itself lasted less than a week but by the end of it 16,000 British soldiers were deployed to the city, most from Britain itself. Some of these had just finished training and thought they were in France when they landed at Dún Laoghaire. At the Battle of Mount Street Bridge a tiny group of Volunteers, about 17 in total, inflicted massive casualties on the British, figures ranging from 150 to 250, including 30 dead. In the greater scheme of things however the Rising had only a limited impact on Britain's ability to prosecute the wider war and the troops were quickly redeployed to recover or move out to fight. The Rising also had a limited impact on Irish troops fighting in the War. Those who were pro Home Rule felt angry at those who took part and others were confused by what had happened. This article and video discusses the reaction of Irish soldiers to the news of the 1916 Rising. German troops did try to make propaganda value out of the Rising, writing up leaflets to the effect that the British were killing Irish people at home. Some of these documents have only came to light recently but I can't find the link to them at the moment.

While many Irish soldiers in the British army would go on to join the Irish Republican Army during the War of Independence (including a Victoria Cross winner) the Rising and British reaction to it had little impact on them during the World War. Whatever they felt later, during the War they were largely apolitical or loyal to Britain, as shown by the tiny numbers of POWs who joined Roger Casements Irish Brigade. Casement hoped to recruit over 500 Irish soldiers from German POW camps but at its peak it numbered 55. Most Irish POWs he spoke before jeered him. Some members of the Irish Brigade remained on in Germany after the War, including Michael Keogh who claims to have saved the life of Adolf Hitler.

I won't post links here but if you are interested I have an Irish history Youtube channel where i discuss the conscription crisis and the German plot in more detail, you can find the links in my comment history.