I've written a short story in which a prosecutor in a case gets romantically involved with a witness for the prosecution, and is subsequently investigated due to the fact that he is in a relationship with a witness, which could possibly motivate him to be more persistent in prosecuting the accused. It's not so much a conflict of interest, but I've searched dictionaries and thesauruses in search of an appropriate term, but haven't found one.
To Llewellyn's point, are you asking for synonyms or alternative means to communicate the concept?
Though admittedly verbose, it could be fun looking for a colorful way to explain the term in regards to the situation at hand. "The Court finds that his external relationship to () provides the opportunity for bias, and thus has decided to disallow his involvement in the proceedings. "