It is not possible to make all new listings appear in the ‘claim listings’ area.
Claim Listings is like ‘temporary’ holding area for the relationship between users and listings.
In most cases, site managers go one of two ways to make use of the feature:
1. Site manager allows users to add listings from the front end, AND also the site manager adds listings and allows users to claim listings OR
2. Site manager does NOT allow users to add listings from the front end, site manager adds all the listings, and ALL listings must be claimed.
If the concern is moderation, the usual recourse is to set new listings to “Draft” status to review them before they are finally published.
To adjust the paid listing status:
https://wpgeodirectory.com/docs/prices-and-payments-add-on-overview/#general