The EU has launched a selection process for the Appellate Body slot that will open up soon:
The second and last term in office of Professor Peter Van den Bossche (Belgium) on the WTO Appellate Body is due to expire on 11 December 2017 and a vacancy will arise.
The European Union (EU) will nominate its candidate(s) for this vacancy on the basis of proposals from EU Member States. The European Commission has requested the Member States to submit such proposals by 3 January 2017.
Interested persons who are nationals of an EU Member State and who meet the requirements for the position of an Appellate Body member are invited to contact the relevant authorities in their Member State for further information (see list of contact points).
The persons proposed by the Member States will be considered by a selection panel, tasked with recommending the most suitable EU candidate(s) from among these persons in view of the requirements laid down in the WTO Agreements. The selection panel is expected to carry out its work as from the beginning of 2017. It will conduct its assessment on the basis of the candidates' curricula vitae and interviews with the short-listed candidates.
This is great transparency. I'm not aware of any other governments who have a public process like this one.