What kind of climbing? Mountaineering or hard technical climbing. If it is mountaineering then the long mountain runs all build much of the fitness you need and these two goals are quite compatible. If it is hard technical climbing then it is much more difficult because training for each of things requires a lot of time on its own. But they are training 2 completely different systems. Long mountain runs need many hours of aerobic training. Shorter, technically hard climbs need strength and muscular endurance in the core and upper body.
It is possible but not easy to do these 2 things at the same time. Best to focus on one then the other.