The Governing Body picks new members.
On a side note, I've been wondering if the creation of the Governing Body was not a measure to avoid ugly power struggles and hostile takeovers that would tend to occur when there's a power vacuum?
I mean, when there is just one figure calling all the shots and that figure dies there's a vacuum that may result in an ugly fight for power and control of the organization such as happened with Rutherford after the death of C.T. Russel. But when you have a Governing Body, power is shared by a collective so the death of an individual never leaves a power vacuum and a political struggle for control. A Governing Body serves to prevent a scenario where there is a complete power vacuum - a scenario that can only occur if all the members died at the same time.
The GB also serves to preserve the status quo and prevent, or at least deter, radical changes from happening. The collective has to agree for any changes to occur and the collective will tend to appoint only those they trust to preserve the status quo. And even if they appoint a rogue, he is only one person and his rogue ideas will be voted down by the collective.
This kind of setup means it is likely that there are lot of secret "lobbying" and behind the scenes dealing and bargaining and quid pro quos among members of the GB to establish majority consensus to get changes agreed on. "You support me on this proposed doctrinal change that I'll table at the next meeting and I'll support your idea to raise the stipends for you and all the members of your committee..."