There was an invasion plan codenamed "Operation Green" which envisaged sending forces to Ireland as part of the planned invasion of Britain. It doesn't seem to have been taken very seriously as the Germans lacked the manpower to divert resources for an unnecessary sideshow.

There was also a plan called "Kathleen" devised by the IRA and suggested by them to the Germans but again the Germans had little interest.

I haven't come across anything concrete about how the Germans planned to run Ireland if they won the war. I suspect it wasn't a high priority. Ireland was militarily insignificant and didn't have anything the Germans needed.