herrschen
to rule
To exercise power over a country or a people, typically as a king, emperor, or dictator.
Der König herrschte über sein Reich mit Weisheit und Strenge.
The king ruled over his realm with wisdom and severity.

to rule / prevail
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to rule
To exercise power over a country or a people, typically as a king, emperor, or dictator.
Der König herrschte über sein Reich mit Weisheit und Strenge.
The king ruled over his realm with wisdom and severity.

The verb 'herrschen' (to rule/prevail) is related to the noun 'der Herr' (the lord, the master). It describes the action of acting like a Herr — that is, exercising power or being dominant.
Der Burgherr herrschte über die gesamte Region.
The lord of the castle ruled over the entire region.
The subject of the sentence reveals the meaning: if the subject is a person (king, dictator), it is about exercising power. If the subject is an abstract condition (silence, chaos, cold), it means 'to be present' or 'to prevail'.
Der Diktator herrschte mit eiserner Hand.
The dictator ruled with an iron fist.
When a person rules over a territory or people, the preposition 'über' with the accusative is always used.
Die Königin herrschte viele Jahre über ein großes Reich.
The queen ruled over a large empire for many years.
To describe a condition or atmosphere, 'herrschen' (to prevail) is very often used with the impersonal pronoun 'es' as the subject. The actual topic then follows in the sentence.
Auf der Party herrschte eine ausgelassene Stimmung.
There was a cheerful mood at the party.
to pass / consist / exist
'bestehen' and 'herrschen' can both express that a condition is present. 'bestehen' sounds more neutral and is often used for rules, problems, dangers, or possibilities. Use 'herrschen' when a condition is clearly noticeable and shapes a situation, for example calm, chaos, fear, or bad weather. Learners may confuse the words because both can sometimes seem like 'es gibt' (there is/there are). As a guide: a danger can 'bestehen' (exist), but in a room silence or unrest 'herrscht' (prevails).

Am Montag herrscht im Büro große Unruhe wegen der neuen Regeln.
On Monday, there is a great deal of unrest in the office because of the new rules.
Bei starkem Regen besteht auf der Straße Unfallgefahr.
In heavy rain, there is a risk of accidents on the road.