To turn a claim and the claims nested under it into an independent discussion of their own, you can extract a claim. If you do this, a new discussion will be created from the extracted claim, and the claim in the original discussion will be converted into a link to the new discussion (see: Linking a Discussion in Another Discussion).
To extract a discussion, click on the three dots that appear at the top-right-hand of a claim when you hover over it, or right-click on the claim, to open the claim menu. Select ‘Extract’, and a window to enter a discussion title will open. Click on ‘create’ to extract the claim.
Note that the Participant Rights and Roles in the new discussion will be the same as in the initial one. The same is true for privacy settings - i.e. a discussion extracted from a private discussion will be set to private and a discussion extracted from a public discussion will be set to public.
Note that extractions are irreversible, so you should take care in selecting the claims you extract.