Après s’être réconciliés, ils se taquinent encore, puis ils rient ensemble.

Because the reconciliation happened before the teasing and laughing.

After après, French often uses the past infinitive to show that one action is completed before the next one:

• après avoir mangé = after eating / after having eaten
• après être parti = after leaving / after having left

Here, the verb is se réconcilier, so the past infinitive becomes:

• s’être réconciliés

So Après s’être réconciliés means After reconciling / After having reconciled.

Because se réconcilier is a reflexive/pronominal verb.

Its basic form is:

• se réconcilier = to make up / to reconcile

When French makes the past infinitive of a reflexive verb, it uses:

• se
  • être
    • past participle

So:

• se réconcilier → s’être réconciliés

The se becomes s’ before être because of the vowel.

It agrees with the people being talked about: ils.

Since the subject is masculine plural (or a mixed group), the past participle is:

• réconciliés

If it were all women, it would be:

• Après s’être réconciliées

If it were singular:

• Après s’être réconcilié = after he reconciled / after making up
• Après s’être réconciliée = after she reconciled / after making up

Se réconcilier means to reconcile, to make up, or to become friends again after an argument.

In this sentence, it suggests that the people had some kind of disagreement or tension, and then they made peace.

So the phrase gives a little story sequence:

1. they reconcile
2. they still tease each other
3. they laugh together

Because se taquiner with a plural subject often means to tease each other.

Compare:

• Ils taquinent Paul. = They tease Paul.
• Ils se taquinent. = They tease each other.

The se gives the idea of a reciprocal action: each person is doing it to the other(s).

So here ils se taquinent encore means something like they still tease each other.

Taquiner usually means to tease, often in a playful, light way.

It is not always harsh or mean. In many contexts, it suggests joking, playful teasing, or friendly needling.

So in this sentence, after making up, they are comfortable enough to joke around again.

Here, encore most naturally means still.

So:

• ils se taquinent encore = they still tease each other

That makes sense in context: even after reconciling, they continue their playful teasing.

Sometimes encore can also mean again, but here still is the better reading.

Because French normally needs the subject pronoun in front of each conjugated verb.

English can say:

• They tease each other, then laugh together.

But French generally says:

• ils se taquinent encore, puis ils rient ensemble

Repeating ils sounds natural and grammatical in French. You usually cannot just leave it out before rient.

Rient is pronounced like ri.

Important point: the -ent ending of ils/elles verbs is usually silent in pronunciation.

So:

• ils rient sounds like il ri

This is the 3rd person plural present of rire:

• je ris
• tu ris
• il/elle rit
• nous rions
• vous riez
• ils/elles rient

Ensemble means together.

So:

• ils rient ensemble = they laugh together

You could say just ils rient, but ensemble adds the idea that they are sharing the moment with each other. It strengthens the sense of closeness after the reconciliation.

Puis means then.

It marks the next step in the sequence:

• Après s’être réconciliés = after making up
• ils se taquinent encore = they still tease each other
• puis ils rient ensemble = then they laugh together

Possible alternatives include:

• ensuite = then / afterwards
• et puis = and then

But puis is a very natural and neat choice here.

Yes.

The main verbs are in the present tense:

• ils se taquinent
• ils rient

But the earlier action is expressed with the past infinitive:

• Après s’être réconciliés

So French is saying:

• first, they reconciled
• now, they tease each other and laugh together

This is a very normal way to show sequence in French.