Hi, welcome!
You can’t do it directly with the component, but you can use CSS to hide links.
There is a .anon class you can rely on to determine whether a user is logged in.
For example, if your link names are “Link 1” and “Link 2”:
/* Logged-out users */
html.anon .link-1-custom-header-links {
display: none;
}
/* Logged-in users */
html:not(.anon) .link-2-custom-header-links {
display: none;
}
The HTML contains a class name where the link name is dasherized, followed by -custom-header-links. You can look at it in the browser console by right click on a link → inspect, you will see:
