sich verzögern
to be delayed
To take place or happen later than planned; to be late.
Aufgrund technischer Probleme wird sich der Abflug um etwa eine Stunde verzögern.
Due to technical problems, the departure will be delayed by about an hour.

to delay
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to be delayed
To take place or happen later than planned; to be late.
Aufgrund technischer Probleme wird sich der Abflug um etwa eine Stunde verzögern.
Due to technical problems, the departure will be delayed by about an hour.

This verb has two important uses: 'sich verzögern' (to be delayed) is reflexive and means that something happens later on its own. 'Etwas verzögern' (to delay something) is transitive and means that someone or something actively causes a delay.
Die Reparatur verzögert sich, weil ein Ersatzteil fehlt.
The repair is delayed because a replacement part is missing.
'Verzögern' (to delay) is an inseparable verb derived from the verb 'zögern' (to hesitate). The prefix 'ver-' here causes a change of state: hesitation turns into an actual delay.
Er hat die Antwort lange verzögert.
He delayed the answer for a long time.
If you want to specify the exact length of the delay, use the preposition 'um' followed by an accusative. The subject of the sentence is the thing that is delayed.
Der Beginn der Veranstaltung hat sich um 30 Minuten verzögert.
The start of the event was delayed by 30 minutes.
With the reflexive use 'sich verzögern' (to be delayed), the subjects are often events, processes, or means of transportation. Common examples are: 'der Abflug' (the departure), 'die Lieferung' (the delivery), 'der Baubeginn' (the start of construction), 'der Zug' (the train), or 'die Antwort' (the answer).
Die Lieferung meiner Bestellung hat sich leider verzögert.
The delivery of my order has unfortunately been delayed.
length
'die Länge' and 'verzögern' can both have to do with time. 'die Länge' describes how long something lasts. 'verzögern' describes that something happens later or moves forward more slowly than planned. They are especially close in the expression 'etwas in die Länge ziehen' (to drag something out): this often means that something lasts unnecessarily longer, similar to 'etwas verzögern' (to delay something). The difference is: 'Länge' names the duration, while 'verzögern' describes the cause or process of becoming later.

Am Montag verzögert sich die Reparatur, weil ein Ersatzteil fehlt.
On Monday, the repair is delayed because a replacement part is missing.
Für die Planung ist die Länge der Prüfung wichtig.
The length of the exam is important for planning.