
die Klausur
written exam
A written exam, usually taken at the end of a semester or course at school or university.
Nächste Woche schreibe ich eine wichtige Klausur in Mathematik.
Next week I'm taking an important written exam in mathematics.
exam / retreat
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written exam
A written exam, usually taken at the end of a semester or course at school or university.
Nächste Woche schreibe ich eine wichtige Klausur in Mathematik.
Next week I'm taking an important written exam in mathematics.

to go into retreat
A closed meeting of a group, for example a party or board, to hold intensive and undisturbed discussions.
Die Regierungskoalition ging für das Wochenende in Klausur, um über den Haushalt zu verhandeln.
The governing coalition went into retreat for the weekend to negotiate the budget.

cloistered life
The state of living in seclusion in a monastery or convent, or the area of a monastery or convent that is not accessible to the public.
Die Nonnen leben in strenger Klausur und haben kaum Kontakt zur Außenwelt.
The nuns live in strict seclusion and have hardly any contact with the outside world.
All meanings of 'Klausur' share one common idea: seclusion or being closed off. Whether it is the closed room for an exam, the closed meeting of a political party, or secluded life in a monastery or convent, it always involves separation from the outside world.
Während der Klausur durfte niemand den Raum verlassen.
During the exam, no one was allowed to leave the room.
In the context of exams, 'Klausur' (written exam) is often combined with the verbs 'schreiben' (to take/write), 'bestehen' (to pass), or 'verhauen' (colloquial for to fail). 'sich auf eine Klausur vorbereiten' (to prepare for a written exam) is also a fixed expression.
Ich muss das ganze Wochenende für meine Klausuren lernen.
I have to study for my exams all weekend.
The expression 'in Klausur gehen' (to go into retreat) is almost always used for political or business bodies. It means that a group withdraws in order to discuss matters intensively and without disturbance.
Der Vorstand ist für zwei Tage in Klausur gegangen, um die neue Strategie zu besprechen.
The board went into retreat for two days to discuss the new strategy.
The meaning 'Leben im Kloster' (life in a monastery or convent) is very specific and is used mainly in religious or historical texts. It is rare in everyday language.
Manche Mönchsorden leben in ewiger Klausur.
Some monastic orders live in perpetual seclusion.
exam / inspection
Both Prüfung and Klausur can refer to a formal test at school or university. Prüfung is the general term for different types of exams, while Klausur specifically means a written exam. When the written format is important, Klausur is appropriate; otherwise, Prüfung is usually sufficient.

Am Ende des Kurses schreibt die Gruppe eine schriftliche Klausur über den gesamten Stoff.
At the end of the course, the group takes a written exam on the entire course material.
Am Ende des Kurses schreibt die Gruppe eine Prüfung über den gesamten Stoff.
At the end of the course, the group takes an exam on the entire course material.