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 design to represent the whole of Ireland. This is a problem when there are many all-Ireland organisations and sporting-teams; some of these compete internationally but cannot use an official 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 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; this has not happened yet but it remains a future possibility. As The Economist notes, this possibility is actually becoming likelier by the day. If the cause for Irish unification escalates or even succeeds, it will need a symbol that is acceptable to both sides.
Therefore, here is my proposal.
Note: My choice of designs do not reflect my political opinions.