nach Belieben
as desired
A fixed expression meaning that you can do something the way you want or think is right; at your own discretion.
Sie können die Soße nach Belieben mit Kräutern verfeinern.
You can refine the sauce with herbs as desired.

to please / to wish
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as desired
A fixed expression meaning that you can do something the way you want or think is right; at your own discretion.
Sie können die Soße nach Belieben mit Kräutern verfeinern.
You can refine the sauce with herbs as desired.

The verb 'belieben' (to please/to wish) is hardly ever conjugated on its own today. It survives almost exclusively in fixed expressions like 'nach Belieben' (as desired) or in the question 'Was beliebt?' (What would you like?), which has a very formal or old-fashioned character.
Fügen Sie Salz und Pfeffer nach Belieben hinzu.
Add salt and pepper as desired.
The verb 'belieben' (to please/to wish) is related to the adjective 'beliebt' (popular). The shared root is the idea of something that pleases, is liked, or is pleasant.
Dieses Lied ist bei jungen Leuten sehr beliebt.
This song is very popular among young people.
The expression 'nach Belieben' (as desired) means 'wie man möchte' (as one likes) or 'nach eigenem Geschmack' (according to one's own taste). It is very frequently used in instructions, especially in recipes.
Du kannst die Zutaten für den Salat nach Belieben variieren.
You can vary the ingredients for the salad as desired.
The question 'Was beliebt?' (What would you like?) or 'Was beliebt Ihnen?' (What would you like?) is very outdated and formal. Nowadays you would hear it only in a historical film or when someone deliberately wants to sound ironic or exaggeratedly polite.
„Was beliebt der Herr zu speisen?“, fragte der Kellner im Scherz.
“What would the gentleman wish to eat?” the waiter asked jokingly.
free
'frei' and 'nach Belieben' both have to do with personal choice. 'frei' is a normal adjective and describes that you are not bound by a fixed rule or obligation. 'nach Belieben' is a fixed expression and means that you may do something however you like. It sounds a little more formal than 'frei' and often appears in instructions, recipes, or offers. For example, you say 'frei wählen' (to choose freely), but 'etwas nach Belieben ändern' (to change something as desired). Both express freedom, but 'nach Belieben' fits especially well with concrete actions.

Die Suppe kann man nach Belieben mit Salz und Pfeffer würzen.
You can season the soup with salt and pepper as desired.
Im Kurs können die Teilnehmer den Platz frei wählen.
In the course, the participants can choose their seats freely.