Nostr is a new protocol that is mainly used as a Twitter-like social network but is flexible enough for a wide array of uses. It also supports encrypted direct messages, which is what clipshift uses for syncing the clipboard between devices. You should generate a new keypair for clipshift using one of the CLI tools (rana, noscl, etc) or nos2x.
In order to avoid taxing public relays, I suggest running a private relay. Nostream is a great option.
Use clipshift config add-backend to be guided through the configuration options or you can manually edit ~/.clipshift/config.yaml and add the following:
backends:
- type: nostr
host: wss://nostr-relay.example.com
user: hex-public-key # technically you don't even need this
pass: hex-private-key
action: sync