The current situation
The island of Ireland is currently split between the Republic of Ireland in the south and Northern Ireland (part of the United Kingdom) in the north. Each side has their own flag, but there is no single neutral design to represent the whole of Ireland. This is a problem when there are many all-Ireland organisations and sporting-teams. Many of these compete internationally but cannot use an official neutral all-Ireland flag because no such design exists. Instead, each one uses their own ad hoc compromise design. A well-known example is the Four Provinces flag (displayed above) that just combines the individual flags of each of Ireland’s four provinces so as to represent the entire island in a disunited, clumsy and complex way.
Compare this situation with the Korean peninsula: Although it is split between North Korea and South Korea, there is a single neutral official flag to represent the whole of Korea for joint organisations and sporting teams.
There is another big reason why an all-Ireland flag is needed. In the future, Northern Ireland may vote to leave the United Kingdom and unite with the rest of Ireland. The Good Friday Agreement stipulates that a referendum for Irish unification can be held if public support is high enough. As The Economist notes, this possibility is actually becoming likelier by the day. If the cause for Irish unification escalates into a realistic possibility, it will require an acceptable symbol that is neutral and not associated with only one side.
Therefore, here is my proposal.
Note: My choice of designs do not reflect my political opinions.