klingeln
to ring
To produce a clear, usually metallic sound, like a bell, an alarm clock, or an old telephone.
Das Telefon klingelt schon seit einer Minute.
The phone has been ringing for a minute already.

to ring
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to ring
To produce a clear, usually metallic sound, like a bell, an alarm clock, or an old telephone.
Das Telefon klingelt schon seit einer Minute.
The phone has been ringing for a minute already.

The subject of the sentence reveals the meaning. If it is a device (e.g. alarm clock, phone), it is about a sound. If it is a person, they are pressing a bell. If it is 'es' (it), it is usually an idiom.
Mein Wecker klingelt jeden Morgen um sechs Uhr.
My alarm clock rings every morning at six.
When referring to a doorbell, the preposition 'an' is often used with the dative to specify the place. But you can also simply say 'klingeln' (to ring).
Kannst du bitte an der Tür klingeln?
Can you please ring the doorbell?
The idiom 'es klingelt bei jemandem' (it rings a bell for someone) has a fixed structure. The 'jemand' (someone) is always in the dative.
Moment, jetzt klingelt es bei mir! Ich weiß, was du meinst.
Wait, now it rings a bell! I know what you mean.
In the expression 'in den Ohren klingeln' (to ring in one's ears), the person who hears the noise is in the dative. The subject is 'es' (it).
Die Musik war so laut, dass mir danach die Ohren geklingelt haben.
The music was so loud that my ears rang afterward.
to understand
'verstehen' and 'klingeln' are only close in meaning in one specific idiom. 'verstehen' is the normal word when you grasp the meaning of something. 'Es klingelt bei jemandem' means figuratively that someone suddenly understands something or remembers something. This expression is rather colloquial and sounds more vivid than 'verstehen'. It is often used when the moment of understanding comes suddenly.

Als der Lehrer den Namen wiederholt, klingelt es bei Anna plötzlich.
When the teacher repeats the name, it suddenly rings a bell for Anna.
Nach dem Beispiel versteht die Familie, warum der Plan geändert wurde.
After the example, the family understands why the plan was changed.