https://grapheneos.org/faq#clipboard
Unless you have a Gboard or other app that can manage clipboard installed, there is not much you can do. What you can do though, after you have used clipboard to paste any sensitive data, you can simply overwrite it by copying any random text. The option of allowing clipboard access in Settings - Privacy is pretty much the only thing you can do out of the box and I would leave that on simply to be notified when currently focused app accessed it.