Interestingly, in 24th Century Star Trek, there are no IGOs, no neutral interstellar organization to which the Federation, Klingon Empire, Romulan Star Empire, Cardassian Union, et al, can go with their disputes. In fact, the only IGO I'm aware of in Star Trek would actually be the Coalition of Planets from the ENT era.
The feature films, in particular, seem to imply that the Federation (despite the potential bias) acts as a de facto
IGO in such disputes. The Klingon Ambassador demands the extradition of "renegade and terrorist" Admiral Kirk before the Federation Council in Star Trek IV,
and the Federation President includes the Romulan Ambassador in discussions around the assassination of Gorkon and its aftermath in Star Trek VI,
even though the Romulans aren't directly involved (to his knowledge at the time, anyway).
OTOH, the subsequent conference takes place on Khitomer because it is "a neutral site," even though it is later known as a Klingon colony, so YMMV...