For a challenge, my club and I have been building a drone with a claw on the bottom. We found a good lightweight claw, but it uses an N20 Geared brushed motor. We have a brushed motor ESC(Quicrun 1625 Brushed) to run it. We currently have a Tekko32 65A ESC set for the main motors of the drone for the brushless motors. The Brushed ESC is rated to 3s, but we have a 4s battery for it. Can we use a capacitor to act as a step down for the Quicrun ESC, and which ports should we wire the ESC to on our FC( Kakute H7 V1)? All the UARTS are available on the FC still, with one plug-and-play slot for ESCs available(motors 5-8).
No, you can't use a capacitor on its own to reduce voltage. You need a voltage regulator. These are often sold as a 'DC to DC converter'. There's a wide range of sizes and current capacities available, and most have an adjustable output voltage.
For low power devices, you can use a 'linear regulator', which simply wastes the unwanted voltage as heat. I'd guess that this would be sufficient for your needs.
Higher power devices switch the power on an off quickly, which is more efficient and doesn't get hot. These are known as 'switching' or 'PWM' regulators, and tend to be a bit larger, heavier and more expensive.
Note that some 'DC to DC converters' are 'boost converters', and are designed to increase voltage instead of decreasing it.