Exoneration, also known as clearing one's name, was the act of proving someone not guilty of a crime.
In 2293, Montgomery Scott felt that any attempts by the crew of USS Enterprise-A to exonerate Captain James T. Kirk by claiming that a cloaked Klingon Bird-of-Prey fired its weapons would be seen as an act of desperation. (Star Trek VI: The Undiscovered Country)
In 2365, when William T. Riker recalled that Q had put the crew of USS Enterprise-D on trial for the crimes of humanity, Q then reminded him they were exonerated for those acts. (TNG: "Q Who")
In 2374, Benjamin Sisko assured Julian Bashir he couldn't exonerate himself by accusing Weyoun of working with Luther Sloan. (DS9: "Inquisition")