I have built a capacitor for a biology experiment, but I need to measure the potential gradient between the plates.
The potential gradient will vary depending upon the things between the plates. In commercial capacitors, the material between the plates is uniform, such as ceramic, mica, a think layer of some oxide etc. However, if the material between the plates is not uniform, the electric field will not be uniform.
For example, if you have a plant between the plates, and you put a device to measure the electric field in the air between the plates, what you are measuring will not be the same as what the plant "experiences". This is because the plant's dialetric constant and electrical resistance differs from the air's. (A dialectric constant refers to how "easily" an electric field passes through a material).
You will encounter the same problem if you have micro-organisms on a drop of water on a slide. The slide and the water will may have different electrical properties from that surrounding your measuring device, although in this case.
With some ingenuity, it may be possible to make the environment of your measuring device similar to that "experienced" by your biological specimen. However, without some thought about this, your readings will likely be wrong.
As for what you can use to measure the the electric field, the answer depends upon whether the field is static or fluctuating. You can sense a fluctuating electric field with another capacitor, i.e. two conductive plates, attached by leads to some measurement device. Static electric fields are more difficult to measure. The classic way is for large electric fields. Large electric fields cause like charged fields to repel. For example your hair standing on end. I don't know of any small instruments or devices that will measure small static electric fields. That doesn't mean there aren't some, and the world has made some pretty small devices lately. It just means I am ignorant of them, and you may get help from other sources.
One work around is to measure the field as you set it up, and assume it remains relatively constant if the voltage between the plates remains constant. That is, sense the change in a capacitor as the voltage across your experimental plates is raised from 0V to your experimental voltage. You will temporarily get a voltage spike across your sense capacitor which you can measure at the time. Or you can measure the current generated by the capacitor as you raise your experimental value and integrate this current over time.