Ulster Tartan

Ulster tartan is basically the only Irish tartan with any historic pedigree. Before Victorian times different tartans didn't represent clans or families  they represented regions. Even this was more by accident than design, it was due to differing styles of local weavers and the limitations of locally sourced natural dyes available. 

Ulster Tartan (peat)

Ulster Tartan (modern)

The Ulster Tartan was re-discovered in 1956 when it was found on a 350 year old pair of trousers (trews) discovered in Dungiven, Co. Londonderry. Experts believe the material may have been designed & woven by Ulster Scots, who were known to be weaving tartan at the time (they mainly used the fabric for shawls & blankets rather than kilts). The trousers themselves are believed to have been tailored in Scotland from the Ulster cloth. Apart from Ulster tartan, practically all other Irish tartans are inventions of the 20th century or later, originating no earlier than the 1960's. There are no historical depictions or descriptions of Gaelic Irish wearing tartan.

Tartan weaving

It's a similar story with Irish kilts. Although they have a slightly older pedigree than most Irish tartan, there is no historical basis for an Irish kilt that goes beyond the formative years of the 20th century or the late Victorian period.  At this time Irish Nationalists caught up in the Gaelic Revival were looking to design a national costume of Ireland. They didn't think the traditional trews or Leine-croich shirt/tunic historically worn by the Gaels looked handsome or heroic enough for modern times so chose instead to adopt the Scottish kilt. So there's no ancient pedigree for an Irishman to wear a kilt, especially a tartan one, unless of course he has Scottish heritage!