What CPU and RAM (qty, speed + DIMM size) do you currently have installed?
I've had a look at the list of compatible CPU's in the HP Z420 quickspecs and their respective performance;
Based on your expected workload and needs (gaming), I would recommend you opt for either the E5-1650 or E5-1660 CPU. Both these CPU's score well in terms of both single-core and all-core speeds. I would also go for 32GB of 1600MHz RAM (4x 8GB or 8x4GB), although you should be able to game reasonably with even 16GB RAM. Whatever fits your budget.
The GPU is also very important for gaming. More VRAM allows higher screen resolutions and/or more detailed textures. If you have a quadro card installed, then you should switch it for a GTX or AMD gaming graphics card.
HP Z620 - Liquid Cooled E5-1680v2 @4.7GHz / 64GB Hynix PC3-14900R 1866MHz / GTX1080Ti FE 11GB / Quadro P2000 5GB / Samsung 256GB PCIe M.2 256GB AHCI / Passmark 9.0 Rating = 7147 / CPU 17461 / 2D 1019 / 3D 14464 / Mem 3153 / Disk 15451 / Single Threaded 2551
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