In empty space, there are no charges to move around. So if there is a non-zero electric field there has to be some stuff around to be the charge that produces the electric field.
So suppose you have some lumps of matter with charges. And then between the matter lumps you have some empty space. You could have an electric field in the empty space.
Now if the electric charges are, overall, balanced plus for minus, they will have some tendency to move to get rid of the electric field. But suppose the charges are a bunch of plus charges on this lump of stuff, and a bunch of negative charges on this other lump. To get from one to the other they would have to get off the lump they start on.
That may require they get over some kind of energy barrier. For example, they may be lower energy on the lump than they would be 1 mm above the lump. They might be lower energy overall if the could move to the other lump. But they have to get over some kind of "speed bump" to get off the lump they start on. If some process or characteristic (such as an orbit for example) is keeping the lumps apart, then the charge balancing might not be all that easy.
So in general, the charge balancing movement could be very slow.
Another possibility is, some processes may affect negative charges (such as electrons) differently to how it affects positive charges (such as atomic nuclei). The larger mass positive charges could get left behind when the electrons get pushed around. Examples might be thermal processes and electromagnetic fields. It is possible that a charge could be built up by different effects on negative or positive charges. As long as this process is acting you might have a charge. Think of the usual example of friction on some such object as glass, plastic, or fur.