This IMRA Carrauntoohil race
Climb (m):1137
Distance (km):12.50
It is an out and back so 1136 mtrs in 6.25Km. It would be easy to get a 1000m in 5Km out of that.
In fact I reckon there would be a number of routes around the 1038 metre summit.
But thinking about it there is a slight drop after the summit of An Cahar, before the final climb to Carrauntoohil. Does it have to be in one continuous climb?
https://www.imra.ie/events/maps/id/1456/