profiles created on one site showing on another site?

There isn’t an automatic way to do that, the listings would need to be updated.

For the example, let’s say listings are created and maintained on the source site. Then they are to be reposted to the target site.
You could;

1. Create the same CPT on the target site
2. Add sample listing and export the listing
3. Return to the source site, export listings
4. Compare the CSV files to make sure they are exactly the same column and column headers, fix CT on target site as needed.
5. Export listings from source site.
6. Import listings to target site

Later on for updates you will need to either A) (recommended) remove all the listings on the target site and re-import an update with all new postings or B) (not recommended) merge them so the source site data is updated with the post_id from the target site to allow updates.

Don’t forget that categories need to match exactly, too.

They should manage their listing on the ‘source’ site, primarily because changes to the ‘target’ site will be overwritten when updates are imported.

GD includes a “Dashboard” function so they can login and find and edit their listings. You can use the “author” field in the listing to assign the listing to the login of the staff member. Users must be promoted to the ‘author’ role first before they can be assigned a listing in the backend. There is also a plugin “Claim Manager Addon” that can facilitate that from the frontend.

Further, be sure to add the Loginbox widget to help your users with navigation on the ‘source’ site to find and edit their listings.

https://wpgeodirectory.com/docs/widgets/#loginbox

I have the full geodirectory package, so then they would be able to manage from the front end?

Definitely

Also, what’s CPT

Custom Post Type (gd_staff?)

If you just have the listings on the target site, then you will also need to setup the target site so they can edit there, but, no, that would not require exporting and then importing.