
vollziehen
to carry out
To carry out or implement an official action, decision, or formal act. This word is mainly used in formal or official contexts.
Der Standesbeamte vollzog die Trauung.
The registrar conducted the wedding ceremony.
to carry out / take place
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to carry out
To carry out or implement an official action, decision, or formal act. This word is mainly used in formal or official contexts.
Der Standesbeamte vollzog die Trauung.
The registrar conducted the wedding ceremony.

to take place
A process or change that takes place or happens, often slowly and profoundly.
In der Gesellschaft vollzieht sich ein Wandel im Umgang mit digitalen Medien.
A shift is taking place in society in how people deal with digital media.

to enforce
To carry out or enforce a court judgment, especially a punishment.
Das Urteil wurde wenige Wochen nach der Verkündung vollzogen.
The judgment was enforced a few weeks after it was announced.
'Vollziehen' is an inseparable verb. The prefix 'voll-' stays firmly attached to the verb in all tenses and sentence types and is never placed at the end of the sentence.
Der Richter vollzieht das Urteil.
The judge enforces the judgment.
This verb belongs to formal language (elevated language, official language). In normal everyday speech, you would use simpler verbs like 'machen' (to do/make), 'ausführen' (to carry out), or 'durchführen' (to carry out/conduct).
Der Priester vollzog die heilige Zeremonie.
The priest conducted the holy ceremony.
In the meaning 'geschehen' (to happen), the verb is always used reflexively with 'sich'. The subject of the sentence is then the process or change itself.
Ein tiefgreifender Wandel vollzieht sich in der Arbeitswelt.
A profound change is taking place in the world of work.
You can recognize the meaning from the sentence structure: the reflexive form 'sich vollziehen' always means 'geschehen' (to happen). If the verb appears with an accusative object such as 'Trauung' (wedding ceremony) or 'Urteil' (judgment), it means 'ausführen' (to carry out).
Ein Generationswechsel vollzieht sich in der Firma.
A generational change is taking place in the company.
In formal contexts, 'vollziehen' is often combined with certain nouns. Typical phrases are 'eine Handlung vollziehen' (to perform an action), 'einen Akt vollziehen' (to carry out an act), or 'eine Wende vollziehen' (to make a shift/turnaround).
Mit dieser Entscheidung vollzog die Regierung eine politische Wende.
With this decision, the government made a political shift.
to occur / take place
For an official measure, „erfolgen“ can describe its occurrence or process. „Vollziehen“, by contrast, emphasizes that an authorized person or body actively carries out or implements the action. When reporting what happens, „erfolgen“ is appropriate; when highlighting the execution, „vollziehen“ is appropriate.

Die Behörde vollzieht die Änderung der Regelung zum ersten Januar.
The authority will implement the change to the regulation on January 1.
Die Änderung der Regelung erfolgt zum ersten Januar.
The change to the regulation will take effect on January 1.