In the conventional sense, there is not exactly something called a tribunal court.
However, a tribunal can assume multiple forms. A tribunal can be an institution with the authority to judge, adjudicate on, or determine claims or disputes. Such institutions may or may not be known or called courts.
However, several institutions are tribunals and have the mandate to function like courts. These can be called or are known as tribunal courts. For example, ICTR or International Criminal Tribunal for Rwanda had the mandate of prosecuting people who were involved in the Rwandan genocide. It involved the typical court proceedings such as presenting evidence in front of the judge. International Criminal Tribunal for Rwanda is not the only tribunal court that had the mandate of prosecuting people who were involved in serious criminal activities. There is also a special tribunal for Lebanon that is investigating the circumstances under which former President Rafic Hariri was assassinated. To deal with crimes in the former Yugoslavia there is an international criminal tribunal for the former Yugoslavia.
There is a significant difference between a court and a tribunal. A tribunal has a specific mandate of individuals or the type of individuals who can be prosecuted. That is not the case with courts. This can be said to be the case with both the International Criminal Court (ICC) and the International court of justice (ICJ). Indeed, the ICC deals with crimes committed by individuals, and the ICJ deals with disputes between nation-states. However, the Rome Statute that governs the conduct of the ICC lists four kinds of activities as crimes. They are genocide, crimes against humanity, war crimes, and the crime of aggression. Crime of aggression was included as a serious criminal offense in 2017. The ICJ is an organ of the UN and thus the UN statute governs the ICJ’s conduct as well as other relevant international law. Therefore, the ICC and ICJ would not be classed as a tribunal because the courts deal with a wide range of cases rather than specific cases and individuals connected to the case.
The most common non-court activity of a tribunal is an award of claims and compensation to businesses. An international tribunal can order multinational companies to seize assets in case governments fail to pay the compensation in case of a business dispute.