The Clipboard API in theory controls access to the system clipboard, but this has security controls around access to it.
The navigator.clipboard.readText() JavaScript command theoretically allows reading the clipboard and is cross-browser compatible, but i’ve not personally gotten this to work (and due to security controls, even testing this via dev. console won’t work, as it needs to be attached to DOM events, and via KAR, didn’t work out a solution either).
If KAR supported keyboard combinations you could have possibly used sendKeys to Control/Command + V the contents, but apparently this is a system-level operation, not browser-level, but at the moment, KAR only supports individual keys via SendKeys.
Hopefully, some of this information may be of use to you!