"Sie ist unabhängig."
Translation:She is independent.
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Unaddicted isn't a word. Take addiction or dependency (note this definition of abhängig) as a condition. If you're not dependent (abhängig) on a person, substance, etc. then you are independent (the Latin prefix 'in-' means not).
I can't think of a word for 'not addicted,' because that is the 'normal' condition - addiction is the change or problem.
As an adjective, that would be unnatural to a native speaker. 'Independent' is the word you would want to use. If you are saying something like "She is not dependent on him for <whatever>", then that works, but to say "She is not dependent" feels like an unfinished thought.
abhängig = dependent, süchtig (nach) = addicted (hooked on drugs). Some people might say they have to have coffee to keep them awake - here you could use either abhängig or süchtig, since it is a dependence/an addiction. Our football game or picnic could be "abhängig vom Wetter", meaning it depends on fair weather to be outside. "Süchtig" will always be addicted (suchen=to search for, seek after).