
dereinst
one day
An elevated expression for an indefinite point in the future; one day, sometime later.
Sie träumt davon, dereinst ein eigenes Haus am Meer zu besitzen.
She dreams of one day owning her own house by the sea.
one day / once
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one day
An elevated expression for an indefinite point in the future; one day, sometime later.
Sie träumt davon, dereinst ein eigenes Haus am Meer zu besitzen.
She dreams of one day owning her own house by the sea.

once
An outdated or literary expression for a point in the past; back then, once, formerly.
Das Reich, das dereinst halb Europa beherrschte, ist längst zerfallen.
The empire that once ruled half of Europe has long since fallen apart.
'Dereinst' (one day/once) is a very elevated and literary expression. It is practically not used in everyday spoken language. It gives a sentence a poetic or solemn tone.
Er hoffte, man würde sich dereinst an seine Taten erinnern.
He hoped that one day people would remember his deeds.
Whether 'dereinst' (one day/once) refers to the future or the past can be recognized from the tense of the verb. If the verb is in the present or future tense, the future is meant. If it is in a past tense such as the preterite or perfect, the past is meant.
Dieses kleine Dorf wird dereinst eine große Stadt sein.
This small village will one day be a big city.
As an adverb, 'dereinst' (one day/once) can stand in position 1, which triggers inversion (verb in position 2). But it can also be placed after the finite verb inside the sentence.
Dereinst werden Roboter viele Aufgaben übernehmen.
One day, robots will take over many tasks.
once / someday
Both words can refer, in elevated language, to an indefinite point in the future. „Einst“ is possible for this purpose, but is less common and less specific, whereas „dereinst“ explicitly means „sometime later“ and sounds more archaic or literary. Use „dereinst“ when this future perspective should be emphasized.

Dereinst wird sie als erfahrene Ärztin in ihre Heimatstadt zurückkehren.
One day, she will return to her hometown as an experienced doctor.
Einst wird man sich an diesen besonderen Tag erinnern.
One day, people will remember this special day.