>>2305928I'll more or less repeat what you have been told, but I hope with better detail.
Pump is provoked by the byproducts of glycogen burning by muscle fibers when they don't have access to oxygen.
Muscle fibers loose access to oxygen when a high effort from your part provokes that they need to contract themselves a lot. Too contracted muscles occlude arteries, blood can't get to the fibers and it's why oxygen can't reach them. Blood flow also cleans the byproduct I mentioned before, which is why you feel better almost instantly when shaking while pumped.
You need to do 3 things:
Strength training (i.e. fingerboarding) - because a bigger muscle increases your anaerobic threshold. This means that the muscle will contract less for a given level of effort, allowing your forearms to work aerobically on the easier parts of a route. Muscles can virtually work for hours aerobically (think of your leg muscles in walking vs. sprinting).
Train continuous endurance (i.e. ARC training) - by climbing a lot under your anaerobic threshold you increase the capilarity on your forearms. This is, you increase the number of capilarity connections between the arteries and the muscle fibers, automatically boosting the amount of oxygen the muscle can receive per time unit. This allows for more efficient burning of oxygen to create energy, allowing the muscle to contract less for a given amount of effort, too.
Just training these 2 energy systems will bring you quite far.
Power endurance training (i.e. 4x4s) - it's inevitable to get pumped while climbing hard. This kind of training will increase the tolerance of the muscle to the glycogen burning byproduct, allowing you to climb for longer above the anaerobic threshold.
Now go out there and train!