If you do not have editing rights in a discussion you will not be able to directly create claims. However, if you follow the same steps as for Creating a Claim you will be able to create a suggested claim, which can be accepted by any Admin of the discussion. Until a suggested claim is accepted it is only visible to you, and Admins of the discussion.
When your suggested claim is accepted or marked for review, you will receive a notification. If your suggestion is marked for review, you will also see any reasons the Admin gave for marking it in the notification and the comments section of the claim. If your claim is marked, you can edit it and resubmit it (see: Editing a Claim).
As an Admin, when someone suggests a claim in one of your discussions, you’ll see a faded claim box with the options to ‘Accept’ or ‘Mark’ the claim. In the top-right-hand of the claim, you’ll see the option to ‘Invite’ the user who suggested the claim to the discussion as an Editor or Writer. To see a list of all suggested claims in one of your discussions, click on the three horizontal bars at the top-left of the screen to open the discussion menu. Click on ‘Suggested Claims’.