seither
since then
Refers to the period from a specific moment in the past up to today; from then on.
Sie zog vor fünf Jahren nach Berlin und wohnt seither dort.
She moved to Berlin five years ago and has lived there since then.

since then
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since then
Refers to the period from a specific moment in the past up to today; from then on.
Sie zog vor fünf Jahren nach Berlin und wohnt seither dort.
She moved to Berlin five years ago and has lived there since then.

'Seither' (since then) is a compound of 'seit' (since) and 'her' (from here/toward here). It literally means 'from that point in time onward' and expresses continuation up to the present.
Er hatte einen Unfall und ist seither sehr vorsichtig.
He had an accident and has been very careful since then.
As an adverb, 'seither' (since then) can appear in different positions in the sentence. If it is in position 1, the conjugated verb follows immediately. It can also come after the verb.
Seither haben wir nichts mehr von ihm gehört.
Since then, we haven't heard anything more from him.
The word 'seither' (since then) only works if a clear event or point in time in the past has been mentioned in the previous sentence or context, which it can refer back to.
Letztes Jahr war ich in Italien. Seither träume ich davon, dorthin zu ziehen.
Last year I was in Italy. Since then, I've dreamed of moving there.
since
'seit' and 'seither' both refer to a period of time that begins in the past and continues until later or up to the present. The most important difference is the grammar. 'seit' is used as a preposition with a time expression or as a conjunction with a subordinate clause: 'seit Montag' (since Monday), 'seit ich hier wohne' (since I have lived here). 'seither' is an adverb and stands on its own in the sentence. It refers back to a previously mentioned point in time. Learners easily confuse the words because both are close to 'seitdem' (since then). As a practical rule: if you mention the starting point directly, use 'seit'. If the starting point is already known, 'seither' can fit.

Du hast die Schule gewechselt; seither wirkst du viel entspannter.
You changed schools; since then you have seemed much more relaxed.
Herr Hoffmann fährt seit dem Unfall nicht mehr mit dem Auto zur Arbeit.
Since the accident, Mr. Hoffmann no longer drives to work.