Edit link in directory results not displaying
In the shortcode when adding a Proile to WP Page/Post there is an option for Search/Public Directory, the shortcode would be something like this

[civicrm component="profile" gid="#" mode="search"]

Replacing the # with the ID of that profile. That provides a page that starts with a search to then view results.

If you include force=1 in the shortcode it will show all results and the search needs to be extended to use to them filter results.

[civicrm component="profile" gid="#" mode="search" force="1"]