That depends on your physiology.

You need to figure out your maximum heart rate. 60-70% of max HR is for recovery, 70-80% is aerobic (requires some effort), 80-90% is anaerobic (burning energy too fast), 90-100% is the "red zone" (burns lots of energy, difficult to maintain for long periods).

Ideally during an event you want to stay in the 60-80% range, and avoid going anaerobic. You can't feel it subjectively, but when you go anaerobic your metabolism changes and you will burn through your readily available blood glucose very quickly; your body also needs to recover from those efforts. So if you're climbing and hit 85% of your max HR, you're working too hard.

Training will not increase your max HR, but it will make it possible for you to do greater efforts for longer periods of time before going anaerobic.