The next candidate for Receiver in Training is Gabriel, then Katharine.
There are a couple of clues that tell you that the next candidate after Jonas is Gabriel. One of these is the fact that all of the Receivers of Memory seem to have light colored eyes. Jonas, the current Receiver in Training, has light colored eyes. Gabe does too. In fact, when Jonas notices this, he feels an instant connection with Gabe.
Now, seeing the newchild and its expression, he was reminded that the light eyes were not only a rarity but gave the one who had them a certain look—what was it? Depth, he decided …He felt self-conscious, realizing that he, too, had that look. (Ch. 3)
The fact that Gabe and Jonas have the same color eyes indicates that they are probably related, meaning they have the same mother. It also means that the traits of Capacities to See Beyond are inherited. Jonas soon learns that Gabe has the ability to accept memories.
He was not aware of giving the memory; but suddenly he realized that it was becoming dimmer, that it was sliding through his hand into the being of the newchild. Gabriel became quiet. Startled, Jonas pulled back what was left of the memory with a burst of will. (Ch. 14)
Even though Gabriel has not been officially chosen as the next Receiver-in-Training, he is already getting memories. He is the one who is currently getting the memories. The only other person who has light eyes is the female five mentioned by Jonas.
Unfortunately, Gabriel does not meet his growth targets. He therefore gets scheduled for release, and Jonas takes him and runs. I guess that leaves the female five (Katharine)! As The Giver says, she is way too young (Six by the time Jonas leaves).
When Jonas and Gabriel leave, Katharine is left with the entire responsibility as the new Receiver-in-Training, at six years old. As The Giver explains, this means the community will need to fend for itself with its memories.
But she's too young. So they will be forced to bear those memories." (Ch. 20)
Jonas’s community is one in which anyone who does fit into the narrow view of the world is eliminated. When Jonas and Gabriel do not follow expectations, they are both eliminated, despite how badly they are needed by the community. Receivers-in-training do not seem to have a very good track record. Look what happened to Rosemary.