Answer:
At there closest points they are about 22 miles or 38 kilometres apart. Cork is Ireland's largest county, so there are parts of it that are a long way from Clare. To go from north Clare to south Cork could be close to 200 miles, if you go by road. A ferry across the Shannon could shorten the journey closer to 150 miles. See the map below of that area of Ireland. County Limerick is between the two counties at their closest points. You would take the ferry from Killimer in county Clare to Tarbert in county Kerry and then continue on to count Cork.