It depends on what you mean and how the HDRI should be working afterwards. To really edit the image itself you should maybe use real image editing software as @Emir suggested.
However, there are things you can do in Blender, depending on what result you want. For example, if you want the bottom half of the HDRI to be simply black (or any other color) you can set the Image Editor to Paint instead of View and paint the lower part. Note that it might not really update in the viewport until you have saved the edited version (and maybe even refreshed with Alt+R). And if you want a seamless transition where the left and right side meet correctly it might be better to do this in Texture Paint mode on a sphere with this texture (because you cannot paint the background):
If the black part reaches too high, you can move the sky down a bit by increasing(!) the Z location of the coordinates with a mapping node:
But if you do not want everything black in the lower part, just overall sky, you could also move the texture even further down by increasing the Z location a lot more. I have not completely removed the landscape so that the principle becomes clear:
The only problem with this method is, the sun in the sky moves down as well as you can see above. And because you only use the upper half of the image for the full sphere, everything gets stretched vertically. Even if you decrease the scale on Z this will not make it look better.
If you don't want to stretch the sky texture and not paint it but rather do everything procedurally in the shader, you could also use a Separate XYZ node to get the Z component of the Generated coordinates. This you can use in a Mix Color node to blend between some color (I've now chosen some blue instead of pure black) and the HDRI. A Color Ramp might help with the transition: