How to sell or replace a frigate?

Solution 1:

According to the hiring section of the page you have linked in your question:

Dismiss unwanted frigates using the middle mouse button from the Manage Fleet panel.

In the control room for your freighter, there is a central command station that you can manage your fleet with. From there, you should be able to do the above and dismiss your frigate (there should be a similar control on console versions of the game as well). There is no warning indication for dismissing the frigate, and you do not getting anything back either.

To get another frigate, simply find another freighter fleet and approach it. You will see a bunch of green icons appear on your screen indicating frigates available for purchase. Once you get close enough, establish communications with the frigate in question and negotiate from there. You can have a max of 30 at a time.