The simple answer - climbing is pumpy. Pump isn’t a sensation that goes away when you get better, particularly not if you’re trying increasingly more difficult climbing. Sure, you may not get as pumped on some easier things, but when trying hard things, it’s almost certain that you will.
If you’re just getting outside again after a training period, there might be another reason. You need to relax. For those first few sessions back on real rock, it’s common to overgrip and put more weight on your arms than on your legs, to stay tense when you should release tension, and to get MORE PUMPED.
It’s fine. As you get back into your groove, it’ll subside a bit.
In this Board Meeting, Nate and I discuss the many reasons why you might still be getting pumped.