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"Succession" star Nicholas Braun says he's not guilty of DUI ... but he has to stay on the wagon while out in the world -- at least for now -- as the case plays out in New Hampshire.

Nicholas authorized his attorney to enter a not guilty plea to the misdemeanor DUI charge he's facing after being arrested last month ... according to new legal docs obtained by TMZ. Everett Collection

The actor had already been released on his own recognizance and now a judge is ordering him to stay away from alcohol, narcotics and controlled substances as the case moves forward.

Nicholas was set to be arraigned Tuesday but we're told he waived arraignment and the trial likely will not happen until January ... so it looks like he's got to lay off the booze for a while. Everett Collecti

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