
clean
Colloquial for the state of not using illegal drugs anymore.
Nach einem schweren Entzug ist er jetzt seit drei Jahren clean.
After a difficult withdrawal, he has now been clean for three years.
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Colloquial for the state of not using illegal drugs anymore.
Nach einem schweren Entzug ist er jetzt seit drei Jahren clean.
After a difficult withdrawal, he has now been clean for three years.

In relation to design or style: simple, minimalist, and without unnecessary decoration.
Das neue Smartphone hat ein sehr cleanes Design ohne sichtbare Tasten.
The new smartphone has a very clean design with no visible buttons.
The adjective 'clean' is usually used predicatively, meaning after a noun with verbs like 'sein' (to be) or 'bleiben' (to remain). It is not declined. Attributive use before the noun is rare and is more likely in a design context.
Er ist stolz darauf, seit zwei Jahren clean zu sein.
He is proud to have been clean for two years.
'Clean' is a word from English that is used in German only for the specific meanings 'drug-free' or 'minimalist'. It is not a general replacement for 'sauber' (clean).
Ich mag den cleanen Look von skandinavischen Möbeln.
I like the clean look of Scandinavian furniture.
The context makes the meaning clear. If 'clean' refers to a person, it is about abstaining from drugs. If it refers to an object, a room, or a style, the meaning is 'simple' or 'minimalist'.
Es ist ein langer Weg, clean zu werden und zu bleiben.
It is a long road to become and stay clean.
dry
Here, both words refer to abstaining from an addictive substance. Trocken is used for a person who previously had alcohol dependence and no longer drinks alcohol. Clean is colloquial and refers to abstaining from illegal drugs.

Nach der Behandlung ist er seit zwei Jahren clean und nimmt keine illegalen Drogen mehr.
After treatment, he has been clean for two years and no longer uses illegal drugs.
Nach der Behandlung ist er seit zwei Jahren trocken und trinkt keinen Alkohol mehr.
After treatment, he has been sober for two years and no longer drinks alcohol.